# Exploring the Presence and Persistence of Cartographic Anchors in Pan-Scalar Maps

Maïeul Gruget, Guillaume Touya, Ian Muehlenhaus

► To cite this version:

Maïeul Gruget, Guillaume Touya, Ian Muehlenhaus. Exploring the Presence and Persistence of Cartographic Anchors in Pan-Scalar Maps. Spatial Cognition and Computation, 2024, 25 (3), pp.195-227. 10.1080/13875868.2024.2383419. hal-04927406

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Submitted on 3 Feb 2025

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<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
EXPLORING THE PRESENCE AND PERSISTENCE OF
CARTOGRAPHIC ANCHORS IN PAN-SCALAR MAPS

THIS IS THE POST-PRINT VERSION OF A PAPER PUBLISHED IN SPATIAL COGNITION AND COMPUTATION
(HTTPS://DOI.ORG/10.1080/13875868.2024.2383419).

Maëul Gruget

<figure><img src="image_2.png" /></figure>

LASTIG, Univ Gustave Eiffel, IGN, ENSG
Champs-sur-Marne, F-77420
maieul.gruget@ign.fr

Guillaume Touya

<figure><img src="image_3.png" /></figure>

LASTIG, Univ Gustave Eiffel, IGN, ENSG
Champs-sur-Marne, F-77420
guillaume.touya@ign.fr

Ian Muehlenhaus

<figure><img src="image_4.png" /></figure>

Esri, Redlands, USA
imuehlenhaus@esri.com

February 3, 2025

ABSTRACT

Within this article, we hypothesise that, in the virtual space of pan-scalar maps, i.e. interactive, multi-scale and zoomable web maps, the map components perceived by the map user during a zoom can mimic the qualities of real-world anchors or landmarks to help the user locate themselves or objects in the map. This article explores the presence and characterizations of these potential cartographic anchors through the analysis of overlapping digital drawings on interactive map views, collected with an online user survey. Our results allow us to identify possible cartographic anchors, characterize them in their stylistic variability, identify similar logics despite variations in localization, and discuss the potential origins of these perceptual comparisons.

**Keywords** cognitive cartography; map design; pan-scalar map; drawing; anchor; landmarks

# 1 Introduction

Sixty years ago Lynch explored people's perception of urban space by asking subjects to draw maps of the city where they live from memory [1]. Behind the wide variety of graphic skills and styles, Lynch found that five types of spatial features were almost always mentioned: "landmarks, nodes, paths, edges, districts". These five cues were later recognized as being individually linked to hierarchies at different levels in human cognitive maps [2, 3, 4, 5, 6], with considerable variation across regions [5]. Nowadays it is generally acknowledged that all of Lynch's elements have some landmarkness (i.e., amount of connection to physical space) and can be measured using an "amount of salience" ranging from 0 to 1 (see [7] for the state of art on landmarkness studies). It is also theorized that those cognitive structures are conceived in a great measure through cartographic perception at different scales [8, 9, 10, 11, 12] but can obviously be structures with direct experiences [13, 14]. Casati points out that the process of drawing can both question and answer visual interpretations about real or imagined delineations [15], based on the assumption that drawing mainly externalizes attention-based cognitive processes – i.e. "modulated by will and attention, operates slowly and stepwise and intensely using working memory" [16]. Montello notes drawing is of methodological interest because it provides insight into the psychological understanding of spatial spaces and scales [17]. Montello, Friedman, and Phillips went on
to explore the vagueness of drawn boundaries [18]. In their experimental study, a group of 93 students drew boundaries on a paper map between what they considered "Southern California" and "Northern California." Each line was then digitized to extract an "empirical mean boundary". In the second study, the state of California and the province of Canada Alberta were divided into hexagons and students were asked to rate between 1 and 10 the degree to which each hexagonal location was "south" or "north". The regular use of sketch maps in spatial cognition supports this idea that drawings can reflect the mental representations [19, 20]. Those "systems of regionalization" [18], reflecting informal ways individuals and cultural groups organize their understanding of the Earth's landscapes, can also help us understand the "breakdown of space into discrete regions" [3]. Individuals vary in how they draw these boundaries, but there can be regional and cultural similarities in how people do so. Nonetheless, the analytical practice of drawing has also been criticized, mainly due to the method's dependence upon a test subject's (1) drawing ability or (2) cartographic familiarity with an area [21]. Nonetheless, studies using drawing analytic tools have shown that it is a useful practice to assess spatiality and more specifically spatial properties such as "location, size, distance, direction, shape, connectivity, overlap, dimensionality, hierarchy and so on" in maps [11, p. 249].

Using the anchor-point theory, Couclelis and colleagues sought to demonstrate the directional and metric distortions induced by certain anchors in cognitive maps. In their experimental approach, the importance of one anchor is not evaluated by frequency, but by its capacity to impact the estimated positions of other secondary cues that are hierarchically bound together. One's house for instance (or one's workplace), because it is a place that people know well, often becomes an important cue binding and impacting other secondary cues in one's cognitive map [3]. They also discuss the way that irregular environments are distorted and remembered as more regular (see [9] for an overview). For example, Milgram and Jodelet have found out with drawings analyses that Parisians both straighten and make parallel city streets and the Seine River [22]. In brief, anchors can be defined as reference points in an environment, which help a moving agent "organize an internal representation of the surrounding space" [23, 24]. We are considering an analogy between a real environment and the multi-scale cartographic space, and we are exploring how these cartographic anchors can act as anchors in this virtual space where we can move vertically by zooming and horizontally by panning.

<figure><img src="image_5.png" /><figcaption>Figure 1: In this map, extracted of OpenStreetMap at zoom level 14 during an exploration of Paris, our first intuitions on pan-scalar anchors are the following: the Seine river, Notre-Dame de Paris, train lines from Gare de Lyon (in the southeast), Jardin du Luxembourg (in the southwest) (source: OpenStreetMap contributors).</figcaption></figure>

In this research, we are interested in the use of what we call pan-scalar maps [12], i.e. interactive, zoomable, multi-scale maps such as Google Maps. It is frequent to feel disorientation when we use these pan-scalar maps, and the absence of consistent landmarks or anchors across scales can be one of the causes of this disorientation [25]. As a consequence, within the virtual environment of a pan-scalar map, we define a pan-scalar anchor as a "cartographic symbol, group of symbols or spatial relation between symbols that is salient or recognizable in all the maps at several consecutive zoom levels." [25]. Pan-scalar anchors are specific landmarks. Like a landmark, a pan-scalar anchor is recognizable in the environment of the pan-scalar map and is also used for spatial orientation, but in a pan-scalar logic that takes user interaction into account [12]. The specificity of the pan-scalar anchors is that they are necessarily stable in zoom. If we look at the map view presented in Figure 1, the Seine River, Notre-Dame de Paris, as well as the main train lines from Gare de Lyon or the Luxembourg Garden, may be perceived as landmarks that can be memorized by many users when they explore this pan-scalar map by zooming and panning around this region; and they remain visible landmarks at
neighboring zoom levels. And the fact that users memorize and retrieve easily these anchors helps them self-localize while exploring the map. On the other hand, the Eiffel Tower in Figure 1, for example, cannot be considered as a pan-scalar anchor because even though it is a landmark at zoom level 14, it disappears at zoom level 13 and loses its stability with zoom. A recent eye-tracking study confirmed that users of pan-scalar maps look at pan-scalar anchors before, during and after a zoom [26].

<figure><img src="image_6.png" /><figcaption>Figure 2: Two consecutive zoom levels of Paris centred on the Eiffel Tower with the IGN map style; the Eiffel Tower recognisable at zoom 14(left) but disappears at zoom 13 (right).</figcaption></figure>

When dealing with human mobility, researchers rather refer to landmarks that can be defined as follows: “Landmarks are geographic objects that structure human mental representations of space.” [7, p. 7]. Landmarks are geographic objects of outstanding visual, cultural or structural properties [24]. We can consider the use of pan-scalar maps as a virtual space that is explored in a similar way as the real space. What Montello [17] calls the vista space is the current view of the map, the environmental space is the set of maps visualize previously during the use of the pan-scalar map, while the geographic space can be seen as the whole set of maps and scales available in the pan-scalar map. If we follow the previous definitions of landmarks, our pan-scalar anchors can be seen as landmarks in the virtual space of the pan-scalar map as they structure our mental representation of space due to their visual, cultural or structural properties in the map.

Standing on the shoulders of existing studies in landmarkness, and inspired by anchor point theory, we propose to define "anchorness" as the propensity of a single map component, to be chosen as a memorable landmark in a map that contains this component. To put it simply, the more people use an anchor, the bigger its anchorness is. Anchorness has a pan-scalar dimension as the use of an anchor during a zoom is directly related to its visibility at each traversed scale. As we are also interested in the usability of an anchor at each scale independently from the others, we define the "anchor intensity" as the importance, the saliency, the memorability of an anchor in a map view, i.e. at a single static scale. We also define the "presence" of an anchor as the spatial extent of the anchor in a given map view. For instance, the Seine River has a very large presence in the map view of Figure 1.

If present in successive views across map zoom levels (e.g., scales), we then define persistence as the evolution of a map component's intensity across successive views (i.e., zoom levels).

Our explicit hypotheses are as follows:

* H1: Consistent pan-scalar anchors exist and can be characterized by their presence, anchorness, intensity and persistence.

* H2: Consistent map components will come to fruition and vary based on how different map styles characterize and represent them (i.e., they will vary based on different cartographic design decisions on different maps of the same area).

* H3: Pan-scalar anchors can present a large anchor intensity even with a small persistence.

* H4: Anchors can have a large presence but a low intensity and conversely.

* H5: Anchors can be either simple map symbols or complex map objects composed of several symbols.

The purpose of this paper is to use the map drawing method to better understand the nature and diversity of such anchors and to simply explore whether certain anchors are consistently drawn. While doing so, we explore whether certain parts of the map are drawn statistically more regularly than others across different viewings. In this exploratory study, as we can see with our five hypotheses, we put an emphasis on the diversity of possible anchors in pan-scalar maps. The
primary purpose of calculating anchor intensity is to find out what is an anchor and what is not in a single map view. We do not plan to compare anchor intensities from different map views. The second point is also to explore our ability to characterize experimentally anchors through drawing.

The remainder of the paper is structured as follows. Section 2 describes the user survey designed to explore this idea of pan-scalar anchors. The following section presents the results of the survey. Section 4 discusses the findings of the survey and some possible reasons that can explain the anchorness of some map features.

# 2 Method

## 2.1 Participants

We wanted users with very diverse ages and experiences with interactive cartography. For recruitment, we first used two large professional mailing lists from the French national mapping agency (IGN) and our university. The survey was also posted on research-oriented mailing lists and also posted to family members and across social media (Twitter, LinkedIn). We have a sample of 174 participants who completed some tasks of the survey, including 102 participants completing the entire survey. We have chosen to keep all the participants' responses, even the unfinished ones because the tasks were independent from each other.

<table><caption>Table 1: Distribution of the declared ages of the participants.</caption><thead><tr><th></th><th>18-24</th><th>25-34</th><th>35-44</th><th>45-59</th><th>60+</th><th>no answer</th></tr></thead><tbody><tr><th>Nb of participants</th><td>11</td><td>53</td><td>49</td><td>39</td><td>8</td><td>14</td></tr></tbody></table>

The gender distribution of participants was also skewed with 107 men, and 45 women (22 preferred not to answer). This imbalance reflects a similar imbalance in the population that was contacted with the mailing lists. We also collected the expertise of the participants with pan-scalar maps 101 participants admitted to using interactive maps daily, while 40 participants only used interactive maps only a few times a week, and 16 only a few times a month. 17 participants preferred not to answer the question. Though we do not have similar numbers for the general public, we consider that the participants in the study are more experts in the use of pan-scalar maps than the general public of users. We had a decent age distribution among participants (Table 1) with 11 aged between 18 and 24, 53 between 25 and 34, 49 between 35 and 44, 39 between 45 and 59, and eight aged 60 and higher. Fourteen participants preferred not to answer about their age.

We also preceded the study with a single Piagetian water-level test, because past experiments showed the test was correlated with spatial skills [27]. 28% of the participants failed the water-level test (44 out of 157, as 18 participants preferred not to complete the test), which is a little below the usual proportion among adults, and confirms that the sample of the study is slightly skewed towards expertise. We chose to limit the survey to desktop computers only, because each participant should have the same view extent to limit variability upon our drawing abilities. We captured the screen size in pixels of the participants and the ones with a small screen (strictly below 12 inches with a default resolution) or a very large one (over 3000 pixels wide) were excluded from our participants.

## 2.2 Materials

In our study, surveyed participants were presented maps of three different places (Paris, France; Madison, Wisconsin, USA; and Bourg-Saint-Maurice Alpes, France), represented in different styles (Google Maps, OpenStreetMap, and IGN France topographic maps), at three different zoom levels (Zoom 11, Zoom 13, Zoom 15). For Paris, two of the three styles are possible, either OSM or Google Maps; for Madison, the two possible styles are either OSM or Google Maps; for Bourg-Saint-Maurice, either the IGN topographic map or Google Maps are possible. We were expecting that most of our participants would live around Paris, due to our recruitment process, so we decided to select a region they would know well, i.e. Paris, and a region that would be unknown for most of them, hence Madison. This is confirmed by the self-declared familiarity with the regions (Table 2). Those two regions also presented environment variety as Madison is a much smaller urban environment than Paris. The Madison region also includes two dominant lakes that appeared as obvious anchors. The Bourg-Saint-Maurice region also presented a different type of topographic landscape with a mountainous region, but was mainly chosen because in this region, the two styles of maps were extremely different, while Google Maps and OpenStreetMap are not that different in Madison and Paris. We limited the number of locations in this study to three for two reasons. First, it provided us with more drawings – and subsequent data – to analyze in each location. Second, fewer locations offered a better user experience for our subjects by limiting the amount of time each would need to spend completing the study.
<table><caption>Table 2: Distribution of the declared experience of the participants with the three map locations.</caption><thead><tr><th></th><th>Paris</th><th>Madison</th><th>Bourg-Saint-Maurice</th></tr></thead><tbody><tr><th>Familiar</th><td>88</td><td>8</td><td>2</td></tr><tr><th>Unfamiliar</th><td>86</td><td>166</td><td>172</td></tr></tbody></table>

The online survey was based on the MapDraw tool [28] (Figure 3). This is not a complex GIS editing tool, but a very simple drawing tool where users just paint the map by moving the mouse cursor. They can change the width of the stroke, and also backtrack their drawing if they want to change it. We did not request precise delineations, but rather rough paintings of the regions of interest. As a consequence, we did not record the stroke of the mouse, but we computed the polygons formed by the painted regions.

<figure><img src="image_7.png" /><figcaption>Figure 3: AnchorWhat survey interface from one of the think-aloud participants at zoom level 13 in Paris with the OSM style.</figcaption></figure>

We created the back-end of the survey instrument using the Django Python framework so that we could store all of the answers in a database, while the client side of the application was developed in Javascript using the OpenLayers library for map rendering. The code of the application is openly accessible on GitHub<fnref n="1" />. The participants gave their informed consent, and the data were collected anonymously to follow the guidelines of GDPR legislation. The data collected during the study is openly available online<fnref n="2" />.

## 2.3 Procedure

To test our hypotheses, we designed a user study where participants were asked to draw on top of the memorable, salient landmarks they saw on the map. It was designed as an online study both to deal with the remaining COVID-19 restrictions and to access a large number of participants. In addition to this online procedure, we invited a few participants to carry out the study with us, with an additional think-aloud instruction [29, 30].

Our study, called AnchorWhat, is a mix of within-subjects and between-subjects designs. Each participant is randomly assigned two of the three regions, and for each region, they are randomly assigned one of the two cartographic styles. Then, each region is processed at three scales: first the smallest scale (zoom level 11), then zoom level 13, and finally zoom level 15. In total, there were 18 different map views drawn by the participants, but each participant only views and draws on 6 of them.

Participants were asked to perform the same task 6 times: drawing the map components they believed they would remember across the different zoom levels, imagining that they were interacting with the pan-scalar map screen captures interactively. For each map view, the participants were asked to draw five different elements. An element does not have

<footnote n="1">¹https://github.com/LostInZoom/lostinzoom-experiments</footnote>

<footnote n="2">²https://www.doi.org/10.5281/zenodo.10213612</footnote>
to be a continuous region, it can be discontinuous elements that make sense together, e.g. two large lakes that are close to each other. Each drawing can be named by the participant, but the name is not mandatory to validate the drawing. Finally, our survey interface permitted the participant to determine a personal "degree of memorability" for each of their drawings: they had three possible values from 'low' to 'strong' with a default value of 'medium'. This degree of memorability was introduced because the participant might perceive elements with a large or small anchorness, and also because five elements were asked for each even though some maps did not contain five obvious salient anchors. Then, users could draw minor elements with a low degree of memorability. Since the survey was online, a recorded video tutorial was presented to the user to demonstrate the functionalities available in the interface and to illustrate the instructions.

## 2.4 Extracting anchors from a collection of drawings

As explained earlier, the purpose of this work is to use the map drawing method to verify our hypotheses on the nature of pan-scalar anchors. From the collection of drawings on each map, we used a three-step method to extract the anchors: (1) find the anchor regions, (2) identify the anchors in these regions, and (3) delineate the anchors from the drawings.

By rasterizing the participant vector drawings and summing the count of each overlapping pixel from all participant drawings, we were able to visualize a heat map of the collection of drawings. Each set of map drawings (by place, style, and zoom level) may then be visualized in two dimensions or three dimensions to better identify the hotspots, i.e. the anchors we are interested in. We visually inspected these heatmaps, and we selected around 10 hotspots per map (Figure 4). As we can see, in this figure, some hotspots are simple connected regions such as the ring road or the Seine River (Figure 4). But others are spatially disconnected such as the major roads or the urban toponyms. We grouped hotspots when it made sense, i.e. when the disconnected parts can be seen as parts of the same anchor and when participants mainly included those parts in a single memorable element.

<figure><img src="image_8.png" /><figcaption>Figure 4: Illustration of the visual inspection of the heatmaps, to find several hotspots, i.e. potential anchors.</figcaption></figure>

For the second step, each hotspot is analysed individually by connecting the map content and the different drawing that form this hotspot of drawings. By this analysis, we identify one or several anchors and we name these anchors. For example, in Figure 5, there is a clear hotspot on the Luxembourg Garden. If one drawing fills in the extent of the Luxembourg Garden, whereas another one only drew merely its toponym, both drawings are still designated as "Luxembourg Garden" because they relate to the same cartographic entity. These denominations were mostly empirical choices although the few think-aloud sessions helped us to understand what participants were drawing. In fact, each drawing could also be named by the participant, which also helped to understand the participant's intention to draw a particular part of the map. Some drawings were removed from the analysis when it was impossible to identify a spatial logic behind the drawing. For instance, it could sometimes be a drawing representing an entity that was too personal to be understood. As anchors may be represented and abstracted differently across scales while still relating to the same entity, we sometimes used a multi-scale definition and denomination. For example, "Urban" corresponds to three
types of cartographic objects in the maps: cities, villages, districts, and urban delimitation. Vegetation corresponded to drawings of natural areas, parks, green spaces, and forests. "Roads" correspond to any type of portion of the road network. "POI" corresponds to any point-based markers in the map.

For the third step, the delineation of the anchor from a set of different drawings, we designed a semi-automated process.
The process computes the average height of the drawings as a basis for the delineation of the anchor:

1. we manually select all the drawings related to one anchor;

2. we intersect each drawing vector polygon with the heatmap;

3. we compute the mean height of the heat map inside each drawing;

4. we compute the mean value of the mean heights for all drawings related to one anchor;

5. we compute the contour line corresponding to this mean height.

For those interested in reproducing this method, we provide a more detailed explanation and a reusable QGIS workflow<fnref n="3" />.

**2.5 Post-processing**

As our analysis of the results is based on the measure of the four indicators presented earlier (*anchorness*, *intensity*, *presence*, *persistence*), this section explains how we can compute them, or at least proxies of these indicators, from a collection of drawings such as the ones we collected during the survey. In Figure 5, 3 map drawing sessions were simulated to explain how these four indicators are measured.

<figure><img src="image_9.png" /><figcaption>Figure 5: Principle for calculating the presence and intensity of pan-scalar anchors. The drawing are simulated.</figcaption></figure>

In this example, 5 elements were drawn by at least one of the participants: the Seine River, Notre-Dame-De-Paris, Luxembourg Garden, Sorbonne University, and Gare de Lyon (train station). We have defined *intensity* as the propensity of a single map component, to be chosen as a memorable landmark in a map view that contains this component. Outside variability in the geometry of the drawing, *intensity* would be dealing with the survey participants’ intention when drawing one map component (i.e. the intention of the participants to draw or choose the Luxembourg Garden for instance) (see the equation below). For this view delimited by the black rectangular border, the Luxembourg Garden is

<footnote n="3">³https://www.doi.org/10.5281/zenodo.10213612</footnote>
drawn 3 times in different ways, Notre-Dame-de-Paris and Gare de Lyon are both drawn 2 times, and the Seine River is drawn only once. Therefore, the resulting intensity becomes 1 for the Luxembourg Garden (3/3), 0.33 for the Seine River having been drawn by only one participant out of three and 0.66 for Notre-Dame-De-Paris and Gare de Lyon having been drawn by two participants out of 3. In the equation, the upper limit for summation corresponds to the number of zoom level under study. For example, as we could see later in our experiment, we only study the zoom levels 11, 13, 15 so the upper limit for summation will be 3.

Equations 1 and 2 present how intensity is computed, following the principles described above.

$$f: ([0, 1], [0, 20]) \to 0, 1$$
$$x, y, \min_{\text{intensity}} \mapsto \begin{cases} 0 & \text{if } X \cap \text{drawing}_i = \emptyset \\ 1 & \text{if } X \cap \text{drawing}_i \neq \emptyset \end{cases} \quad (1)$$

$$\text{intensity}(x) = \frac{\sum_{i=1}^{n} f(i, x)}{n} \quad (2)$$

Where x is an anchor, n is the number of participants, and drawing_i is the union of drawings of the i^th^ participant.

The presence of an anchor is the spatial extent of the anchor in a given map view (see Equation 3). The extent of the anchor is the area of the delineation of the anchor (see previous sub-section) divided by the area of the map view. For instance, the Seine River drawing has an area of 617,272 m² when the area of the view (i.e. delimited in black) is 1,1607,818 m². The drawing of the Seine River by Participant 2, therefore, corresponds to 5.4% of the view. The presence of the Seine would therefore be 0.054 for this view. The two drawings of the Gare de Lyon have an average delineation with an area of 188,804 m², i.e. 1.6% of the view, resulting in a presence of 0.016.

$$\text{presence} = \frac{\text{area}_{\text{anchor}}}{\text{area}_{\text{view}}} \quad (3)$$

If present in successive views across map zoom levels (e.g., scales), we also have defined persistence as the evolution of the intensity of an anchor across successive views (i.e., zoom levels). First, for a given intensity threshold you are interested in, the function g tells you if anchor x is intense enough to be an anchor at zoom level z (Equation 4). Then the number of persistent scales p counts the number of zoom levels where a given anchor has its intensity above the threshold, among the ones that were studied (Equation 5).

$$g: ([0, 1], [0, 20]) \to 0, 1$$
$$x, y, \min_{\text{intensity}} \mapsto \begin{cases} 0 & \text{if } \text{intensity}(x, z) < \min_{\text{intensity}} \\ 1 & \text{if } \text{intensity}(x, z) \ge \min_{\text{intensity}} \end{cases} \quad (4)$$

Where x is an anchor of the map, z a zoom level between 0 and 20, min\_intensity the minimum intensity of an anchor to be considered as usable, and intensity(x, z) is the intensity of anchor x at zoom level z.

$$p: [0, 1] \to \mathbb{N}$$
$$x \mapsto \sum_{z \in Z} \frac{g(x, z)}{|Z|} \quad \text{where} \quad Z \subseteq [0, 20] \quad (5)$$

Finally, the anchorness sums the intensity values across all zoom levels (Equation 6).

$$\text{anchorness}(x) = \sum_{z \in Z} \frac{\text{intensity}(x, z)}{|Z|} \quad \text{where} \quad Z \subseteq [0, 20] \quad (6)$$

If we come back to the example of Figure 5, if the Seine River is drawn by 2 out of three participants in another view and not at other zoom levels, the Seine River will then have an intensity of 0.33 at the zoom level of the figure 5, and 0.66 at this other zoom level. The intensity is null at all the other zoom levels. Then, the number of persistent scales p is 2/21, and the anchorness is 0.047(0.99/21).
Moreover, certain map components also seem to be conceived by many participants as spatially bounded, linked. As explained in the procedure of the survey, the interface allowed participants to draw multiple disconnected cartographic elements using the same hue. For example, the wooded areas of Boulogne and Vincennes in Paris — two geographically distinct and separate areas of the city — can be considered as a single complex anchor. One of the think-aloud participants mentioned that these two areas had the "same function" and "the same size".

We propose that spatial relation is an additional aspect of anchorness (i.e., spatial relation anchorness). We define it as the propensity of an identified combination of map components to be drawn jointly with one another, i.e., the occurrence of distinct map components being mentally combined into single map components divided by the total number of participants of a view in the study. For instance, if 20 out of 40 participants draw the two wooded areas with the same hue, the resulting spatial relation anchorness is 0.5.

## 3 Results

In this section, we present the results from the AnchorWhat survey with the anchors extracted in the 18 maps (3 regions, 3 scales, 2 styles). However, we limited the visual presentation of the results to the maps with the Google style. All the other drawings, as well as the initial maps presented to the participants are openly available on the Zenodo repository of the study.

<figure><img src="image_10.png" /><figcaption>Figure 6: 3D heatmap of the drawings on Paris at zoom level 11 with Google style and the anchors identified.</figcaption></figure>

We computed the intensity, the presence, the persistence and the anchorness of all these anchors, and we also analysed the anchors that are spatially related. The 3D maps that helped us extracting the anchors are presented and the measured values of presence, intensity and anchorness are presented for Paris from Figure 6 to Figure 8, for Madison from Figure 10 to Figure 12, and for Bourg-Saint-Maurice from Figure 15 to Figure ??.
<figure><img src="image_11.png" /><figcaption>Figure 7: 3D heatmap of the drawings on Paris at zoom level 13 with Google style and the anchors identified.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Figure 8: 3D heatmap of the drawings on Paris at zoom level 15 with Google style and the anchors identified.</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>Figure 9: Synthesis of the measures on anchors in the Paris maps with Google style. Red is for zoom level 11, orange is for zoom level 13, and yellow for zoom level 15. Presence is presented as a percentage.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Figure 10: 3D heatmap of the drawings on Madison at zoom 11 with Google style and the anchors identified.</figcaption></figure>
The results of the AnchorWhat survey validate H1 (i.e. there are pan-scalar anchors): some map parts are effectively more drawn than others and can be characterized by their presence (i.e. the average extent of the drawings on a map view), their intensity (the propensity that a hypothetical element is highlighted), spatial relations anchorness (i.e. the propensity that a combination of elements is highlighted in the same hue), persistence (i.e. the number of scales where an anchor is intense enough), and their anchorness (i.e. the sum of the intensities at multiple scales). For example, the Lakes in Madison with Google style have an intensity of 0.375 at zoom level 11 (Figure 10), 0.42 at zoom level 13 (Figure 11) and still an intensity of 0.26 at zoom level 15 (Figure 12) with a resulting persistence of 3 and an anchorness of (1.055/3) = 0.35 (Figure 13).

<figure><img src="image_15.png" /><figcaption>Figure 11: 3D heatmap of the drawings on Madison at zoom 13 with Google style and the anchors identified.</figcaption></figure>
<figure><img src="image_16.png" /><figcaption>Figure 12: 3D heatmap of the drawings on Madison at zoom 15 with Google style and the anchors identified.</figcaption></figure>

The results also validate H3, as we can clearly see some anchors with low persistence, even though they have high intensity at some scale, and some other anchors with high persistence, despite a medium intensity. For instance, in Bourg-Saint-Maurice with the Google style at zoom level 13 (Figure 16), the ski station is extremely salient with an intensity of 0.7 (Figure 18) and is not at all at zoom 11. However, we cannot say that it is not persistent in the zoom 15, as the view at zoom 15 is not centered on the sky station (Figure 15). At the same time, in the same maps, the roads have a high intensity at each zoom level, giving an anchorness value of $(1.75/3)=0.58$.
<figure><img src="image_17.png" /><figcaption>Figure 13: Synthesis of the measures on anchors in the Madison maps with Google style. Red is for zoom level 11, orange is for zoom level 13, and yellow for zoom level 15. Presence is presented as a percentage.</figcaption></figure>

The results also support H4 about the absence of a correlation between presence and intensity. For instance, the city toponyms in Paris, grouped in the spatial relation between anchors "Urban" in Figure 9, or 'Bois de Vincennes' at zoom level 11 in Paris, have a low presence but a very large intensity at all scales with the Google style, and thus a large anchorness. On the other hand, there are anchors with a large presence but a smaller intensity, e.g. the ring road in Paris at zoom level 13 with Google style in Figure 14, or the lakes in Madison at zoom level 15 with both styles in Figure 12.
<figure><img src="image_18.png" /><figcaption>Figure 14: 3D heatmap of the drawings on Bourg-Saint-Maurice at zoom 11 with Google style.</figcaption></figure>

Finally, the results of the survey also support H5. Some anchors are simple map objects such as the Eiffel Tower in Paris with the Google style or the Bourg-Saint-Maurice toponym with both styles. But the results show that anchors are more often complex objects, composed of several map objects that are either grouped perceptually following Gestalt principles (e.g. the ring road in Paris with both styles) or logically (e.g. the airport in Paris, composed of a plane symbols, runways and taxiways).

<figure><img src="image_19.png" /><figcaption>Figure 15: 3D heatmap of the drawings on Bourg-Saint-Maurice at zoom 13 with Google style.</figcaption></figure>
<figure><img src="image_20.png" /><figcaption>Figure 16: 3D heatmap of the drawings on Bourg-Saint-Maurice at zoom 15 with Google style.</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>Figure 17: Synthesis of the measures on anchors in the Bourg-Saint-Maurice maps with Google style. Red is for zoom level 11, orange is for zoom level 13, and yellow for zoom level 15. Presence is presented as a percentage.</figcaption></figure>
Finally, the second hypothesis also seems to hold true, as the list of anchors, as well as their anchorness varies with style. For example, the Eiffel Tower has a higher intensity with Google Maps at zoom level 13 compared to the OSM style (Figure 18). The train lines and train stations have a higher anchorness with OSM in Paris, probably because they are much more salient with the OSM style compared to Google style (Figure 18).

<figure><img src="image_22.png" /><figcaption>Figure 18: Two 3D heatmaps of the drawings on Paris at zoom level 13 with Google (on the top) and OSM (on the bottom) styles. The three highlighted anchors, the Eiffel Tower (1), train lines and train stations (2), and ‘Bois de Vincennes’ (3) show similarities and differences between the anchors recognized with both styles.</figcaption></figure>

The spatial relation between the lakes Roselend and Chevril in Bourg-Saint-Maurice is an anchor only with the Google style, with a high intensity. Conversely, some anchors share similar intensity values in the two styles in the three tested locations. For instance, in the Paris maps at zoom levels 11 and 13 (Figure 18), the ring road and the two wooded areas ‘Bois de Vincennes’ and ‘Bois de Boulogne’ have similar intensity values with OSM and Google styles. We can note also that the persistence of the lakes in the Madison maps is similar with both styles. And this is not restricted to the comparison of Google and OSM styles, because in Bourg-Saint-Maurice, hydrography has a similar anchorness with the Google and the IGN styles which are clearly different from each other (Figure 19).
<figure><img src="image_23.png" /><figcaption>Figure 19: Lake Roselend near Bourg-Saint-Maurice in the IGN and Google styles. The difference of saliency explains why it was considered intense with Google style and not with IGN style.</figcaption></figure>

With these results, we can also identify common anchor types in all three locations. The most demonstrative example is hydrography whether it is a large river or a large lake. In Bourg-Saint-Maurice with the Google style, the lake has an intensity of 0.23 at zoom level 11, and then the river has an intensity of 0.58 at zoom level 13 and 0.91 at zoom level 15. Lakes in Madison with Google style have an intensity of 0.38 at zoom level 11 and 0.41 at zoom level 13, 0.23 at zoom level 15. The Seine River in Paris has an intensity of 0.58 at zoom level 11, 0.79 at zoom level 13 and 0.53 at zoom level 15 with the Google style. It seems that, whatever the place, or even the style of the topographic map, large rivers and large lakes tend to be important and persistent anchors.

In the following illustration (Figure 20), each line corresponds to the bounding of two cartographic elements that were drawn in the same hue by at least one participant. This example shows that there can be patterns of anchors that make even more sense as a group than considered individually. The group of lakes in Madison forms what Mackaness calls a "geographic phenomenon" that is perceived as such by the map reader [8]. In our three maps, the lakes Figure 13 are first linked as a "group of lakes" at zoom level 11 according to a think-aloud participant, with an intensity of 0.23, then evolve as a spatial relation between the two central lakes "on both sides of the city" (lakes Mendota-Monona) at zoom level 15 with an intensity of 0.42, because only those two lakes are visible at this scale. At zoom level 13, a phase of transition seems to be identified as 7% of participants drew the 4 lakes together, while 32% of participants only drew
lakes Mendota and Monona together (Figure 20). This can be explained by the fact that only a small portion of Lake Waubesa is visible in the zoom level 13 view.

<figure><img src="image_24.png" /><figcaption>Figure 20: Bounds of lakes and vegetation at Madison OSM style, between zoom 13 and zoom 15. Each link corresponds to 2 map parts having been drawn with the same hue by one participant.</figcaption></figure>

During the survey, we asked the participants to mention their knowledge of the three places Paris, Madison and Bourg-Saint-Maurice, to differentiate the ones living or having lived in the location, and the others. The main difference between participants familiar with Paris and unfamiliar with Paris is that familiar participants experienced the space depicted on the map. We can visualize the differences in the drawing of the two groups with a 3D elevation map (Figure 21).
<figure><img src="image_25.png" /><figcaption>Figure 21: Drawing elevation difference between participants familiar with Paris and unfamiliar with Paris with OSM map (top image) and Google Map (bottom image) at zoom level 15 in Paris. Spaces with positive elevation correspond to spaces more drawn by participants familiar with Paris. Identification of two spaces, "Les Halles" and "Les Invalides", more drawn by familiar participants.</figcaption></figure>

This figure shows the differences in Paris at zoom level 15 with both styles. Though the differences are not the same at both styles, there are clearly differences in the anchors drawn by participants familiar with Paris and unfamiliar with Paris. For instance, familiar participants drew more the Invalides esplanade on the OSM map (number 1 on Figure 21), or 'Les Halles', a large and central shopping mall, on the Google map (number 2 on Figure 21). Even though our study design cannot help us interpret these differences, we can refer to the three types of landmarks: visual, cognitive and structural landmarks [24]. Visual and structural landmarks should be identified similarly by participants familiar with Paris and unfamiliar, so the differences might come from cognitive anchors, i.e. anchors selected because of the personal experience of space by the participant. If Parisians are used to shopping in 'Les Halles', they are also used to use this as an anchor in a map, even though it is not particularly visually salient.

# 4 Discussion

## 4.1 What explains anchorness

In this section, we discuss what could possibly explain some of the high and low anchorness values of the map components. First, one of the think-aloud participants suggests that the centrality of the anchor they are drawing (the Seine river in Paris), i.e. the fact that it is located near the center of the view, is the main reason why they chose it ("The Seine is a very strong anchor. I don't know exactly why, but it is large and central"). Similar comments were made about the lakes in Madison at zoom level 11. Centrality is known to be a positive factor in saliency models [31], and it seems to be also the case for anchors. However, we chose to centre our map views on some of the main anchors we were anticipating, so in the map views of the study, the anchors are mainly in the center of the view and the corners are devoid of anchors. We would need for instance to have Paris in a corner, to assess the influence of centrality on the intensity of the anchors.
<figure><img src="image_26.png" /><figcaption>Figure 22: Elevation representation from superimposed drawings for the four lakes in Madison at zoom level 11. The only labelled lake (Lake Waubesa) is the one standing out.</figcaption></figure>

It also seems that the text on the map has a positive influence on the anchorness, i.e. when an anchor contains text that describes or names the anchor, its anchorness is larger. Though the survey cannot validate such a hypothesis, it shows hints with the comparison of two map styles on the same region. For instance, in Madison at zoom level 11, Lake Waubesa has a toponym only in Google, and it is clearly more drawn as an anchor than the other lake without toponyms (Figure 22).

We know that our vision is able to grasp groups of visual elements that follow so-called Gestalt grouping principles such as similarity, continuity, closure or symmetry [32]. As a consequence, spatial configurations of anchors following these principles tend to be more visible and memorable. Figure 23 shows an example where the think-aloud participant noted the parallelism and the symmetry between the roads drawn in brown and red.

<figure><img src="image_27.png" /><figcaption>Figure 23: Drawing tasks from a think-aloud participant on Madison with OSM map style at zoom level 15. The participant emphasized the memorability of these two roads, also because of their parallel and central quality in the map view.</figcaption></figure>

Another factor that can explain anchorness is the uniqueness and/or the regularity of the geometry of the anchor. For instance, one of the think-aloud participants commented on the choice of the ring road around Disneyland in Paris that it was "a perfect circle and memorable because of the shape".

## 4.2 Scale and anchors

The presence of the anchors in the map view somehow related to their spatial extent in the field, though some specific anchors such as the Eiffel Tower may benefit from a symbol much larger than their spatial extent. Then, when scale
decreases, their spatial extent might become too small to remain intense enough in the map. But in the other way round, what happens with anchors when their presence tends to 1? We make the assumption that these anchors become cognitive regions instead, and do not directly act as anchors anymore. For instance, Paris and its toponym are major anchors at zoom level 11 and also at smaller zoom levels, but when it comes to zoom level 15, we are in Paris, it is no longer an anchor, but a cognitive region we know we are “located” in. Nonetheless, the anchor still plays a role as we know that only the anchors previously located inside Paris will be usable now. Figure 24 shows another interesting example with the two bigger lakes surrounding the center of Madison. According to our results the lakes intensity drops to 0.4, because their massive presence transforms them into a background a map, which does not draw the visual attention of the reader. We tend to see them more from the peripheral vision but there is less need to use them as landmarks anymore. As a consequence, we can argue that the persistence of anchors may never tend to one because they all tend to fade at some point at small and large scales.

<figure><img src="image_28.png" /><figcaption>Figure 24: Extract of the Madison map at zoom level 15 with OSM style. At this scale, the lakes are a less intense anchor according to our results, despite their massive presence in the view.</figcaption></figure>

## 4.3 Self-localization in interactive maps

In a previous study, we claimed that interactive, multi-scale, zoomable maps are better described as pan-scalar maps because they are designed with the assumption that you will necessarily zoom back and forth across many scales to actually use them effectively [12]. What differentiates pan-scalar maps from other online or printed maps is that the cartographic representations at different scales are never meant to be consumed individually. They are part of a pan-scalar cartographic product, allowing the user to self-localize within the map product across both space (horizontally) and scale (vertically). In brief, what made them panoptic by design is that one view at one scale could always be conceived both inter-visibly and independently of varying views at the same scale (via horizontal panning) or across different geographic scales (vertically). Pan-scalar map design takes into account what one could have remembered in previously perceived views or may yet access via interaction. Pan-scalar studies give a name to and directly address concerns raised in previous studies regarding disorientation in interactive, multi-scale, zoomable maps [25].

It has been argued that disorientation occurs during the exploration of a pan-scalar map when people are consciously aware that they do not know where the place depicted on a map is exactly and/or where they need to go (horizontally or vertically) to achieve a more useful map view [25]. This feeling of disorientation is often revealed via the awareness of our inability (or at least struggle) to construct a mental representation from cartographic communication alone (i.e., merely by looking at the map). Mackaness has argued that "map stability" is linked to the way patterns, among phenomena, persist over large changes in scales [8].

We make the assumption that the persistence and anchorness of map components in a succession of views is linked to self-localization and of imperative importance for helping map users maintain spatial knowledge across a succession of interactive views. By identifying common map components that act as pan-scalar anchors, cartographers could help map users self-localize where they are in a pan-scalar map across multiple scales and horizontal pans. For example, from our sample, it appears in Paris that the Seine River, the ring road, 'Bois de Vincennes', and 'Bois de Boulogne' may work as preferred anchors because of their combined anchorness and persistence. In Madison, Wisconsin, the lakes, the city boundary, the main roads, vegetation, and Capitol Square seem to be good pan-scalar anchors. In Bourg-Saint-Maurice,
hydrographic features, arterial roads, and the Bourg-Saint-Maurice toponym seem to be the best anchors. We plan to test this assumption in future studies.

As a design recommendation, for instance, our results show that the Seine River has a lesser intensity at zoom level 11 (0.28) than at zoom level 13 (0.73), or at zoom level 15 (0.68) on the OSM map. The intensity of the Seine River with Google Maps at different zoom levels varies from OSM, though — 0.58 at zoom level 11, 0.68 at zoom level 13, and 0.68 at zoom level 15. In this regard, the Seine River's persistence in the Google Map Style is seen as more "homogenized" and continuous. During a pan-scalar exploration across scales, the change of intensity of the river in OSM might be perceived as a break and trigger disorientation. In this example, our pan-scalar map design recommendation is that the OSM map would benefit from a redesign. It should attempt to make the Seine River, and more generally all similarly large rivers, "more perceptible" at zoom level 11 to help the user perceptively link the river across scales during these successive interactive views.

We also argue that such definitions can be extended to spatial relations. We propose that the spatial relationship between map components is also linked to self-localization, e.g., the spatial relationship of the two lakes in Madison from zoom level 13 to zoom level 15. We hypothesize that some spatial relationships, such as the one between the two lakes, must also be considered cartographic anchors in the virtual space of a pan-scalar map. If Lake Mendota changes from blue to green during the succession zooming across views, the topological bounds would maintain the relationship but the loss of semantic logic may counter this spatial relationship's persistence. We argue that self-localization during successive views may benefit from maintaining the perception of the spatial relationship, which has been shown in many forms of map modelling [33].

Using this logic and based on our study, we can identify some spatial relationships between cartographic elements that might be considered pan-scalar anchors. In Paris, the relation between 'Bois de Boulogne' and 'Bois de Vincennes' is one, as well as the spatial relationship between train lines and train stations. In Madison, Wisconsin, the spatial relationships between lakes, roads, and the polygons representing the parks along the shores, are ripe for highlighting. In Bourg-Saint-Maurice, highlighting the spatial relationships between particular points of interest, rare urban entities, and the interesting variety of hydro systems would be ideal.

In previous work, we discussed the way that pan-scalar maps are global in scope. Due to automation, they will frequently use exactly the same design and generalization rules for every place in the world [12]. Yet, there can be important landscape differences that would benefit from environment-aware design rules, requiring different levels of detail. While designing pan-scalar maps, using our methodologies in specific environments may help map users foster a more robust understanding of the spatial environment across scales and determine specific needs for environment-aware design rules. For instance, some rivers (or parts of a river) may not need the same anchorness or persistence that the Seine River requires crossing through a pan-scalar map of Paris.

We can also make the hypotheses that how we perceive one view is also determined by what we have seen previously. For instance, the Seine River anchorness at zoom levels 13 and 15 very likely incorporates and is partially determined by how a subject perceives the river at zoom level 11. But we also suspect a similar learning effect while zooming out. The succession of accumulated perceived views, we argue, is a key component to understanding the intensity of a map component in any single view.

# 5 Conclusion and further directions

As a conclusion, this paper explores the concept of pan-scalar anchors, and how it can be theoretically and experimentally characterised. People identify similar anchors, whether simple map objects such as the Eiffel Tower symbol, or more complex group of objects such as the ring road in Paris. Our methodology based on digital drawings on top of a map proved to be adapted to collect mental representations of the map such as the pan-scalar anchors. For instance, by validating our first hypothesis, we have shown that analytic drawing tools can successfully identify potential cartographic anchors across a succession of map views. We have also shown that style variations can have a direct impact on a person's characterization of a map anchor, whereas certain anchors will persist despite differences in map style. Our third hypothesis is also validated, certain parts of maps in certain areas maintain a high level of anchorness despite their weak presence or representation (e.g., 'Bois de Vincennes' at zoom level 11 in Paris) or conversely have a low level of anchorness despite their dominant presence (e.g., the large lakes in Madison at zoom level 15). In these cases, anchorness is not fully correlated to the presence of the element in the map view. With this exploratory work, we have identified a number of variables that seem to influence the anchorness of a map component. For example, if the three views had been given in a different order, the landmarks drawn by the participants could have been different. In a pan-scalar logic, it would be interesting to measure the intensity variation of an anchor depending on the previously visited map views. Rather than remaining declarative by asking participants to predict what they would remember, we could also quantitatively verify what is actually memorable, for example by verifying if persistent anchors are more
often remembered than less persistent ones. Moreover, text or labels in pan-scalar maps seem to have a positive influence on anchorness. Unfortunately, at this time, and given the constraints of the study, we are unable to statistically isolate these variables. What exactly explains the anchorness values we measured? Knowledge about the local environment? What users have previously seen on other maps or in media? The centrality of a given anchor in the map view? The unique nature of the anchor? The spatial relations among potential cartographic anchors? Or perhaps something completely different? We see this exploratory study as an avenue for further research.

Within this article, we also proposed extending, or at least enhancing, our definition of anchorness. Such an extension would include adding a component of how much one map component is perceivable in one view versus others — i.e., its persistence across a succession of pan-scalar views. We argue that pan-scalar map self-localization is very much about maintaining the perception of map components during a succession of views. We believe that the methodology used here, and our (largely automated) analysis, will also benefit map designers and practitioners (i.e., cartographers). Cartographers may want to start evaluating their core users’ perceptive needs while engaging with pan-scalar maps for more effective map design and a better overall user experience. We are also convinced that there is more to analyse in the results of the study. For instance, we are interested in analyzing the content of the empty spaces, i.e. the areas of the map that were never drawn by the participants, to understand what anchors are not. Similarly, it would be interesting to study the regions that were drawn only once or twice. If we look at how sketch maps can be analysed [34], it would be interesting to apply a similar methodology to our drawings; for instance, looking at the degree of generalisation of the drawings compared to the map could be interesting [35]. Finally, now that we have a better idea of what pan-scalar maps are, we are interested in the automated recognition of the anchors using deep learning models [36].

## Funding

This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 101003012).

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