Proceedings of 4th International Symposium for Color Science and Art 2023

Spatial color mixing and color illusions
Akiyoshi Kitaoka
Faculty of Comprehensive Psychology, Ritsumeikan University, 2-150 Iwakura-cho, Ibaraki, Osaka 567-8570, JapanABSTRACT
Any color can be made from black and white stripes. In
this article, I will explain the principles of color illusion
based upon spatial color mixing and show how it is created.
1. INTRODUCTION
Color illusions can be classified into color assimilationand color contrast. Both are hue illusions. Colorassimilation is a phenomenon in which the color of a target
area is perceived as the same hue as the surroundingcolor. Fig. 1 shows an example.

Fig. 1 This picture is grayscale; however, by placingcolored lines on it, it appears a color image.
Color contrast is a phenomenon in which the hue of thetarget area is perceived in the opposite direction to that of
the surrounding colors. Fig. 2 shows an example.

Here, I introduce a new color illusion based on spatialcolor mixing. This color illusion has properties of bothassimilation and contrast.
2. SPATIAL COLOR MIXING
Studies have shown that if three appropriate colors arechosen, a full-color image can be represented. These
primary colors are typically red, green, and blue. They canbe mixed by projecting them in the same location, or byplacing them side by side. The latter is referred to as
spatial color mixing. Fig. 3 shows an example of this.

Fig. 3 This image is composed of lines of threecolors: red, green, and blue.
As spatial color mixing involves three primary colors
being placed side by side, it allows room for each color tomix with the other two. What happens if we add green tothe red lines, blue to the green lines, and red to the bluelines? Subsequently, Fig. 4 is obtained. Although Fig. 4 isbrighter than Fig. 3 because of the added colors, there is
no issue with its appearance [1].

Fig. 2 The window area of this train appears red;
however, none of the pixels have a red hue; they are
all gray, grayish blue-green, or grayish green.
Fig. 4 This image is composed of lines of threecolors: yellow to green, cyan to blue, and magenta tored.

Proceedings of 4th International Symposium for Color Science and Art 2023
Moreover, what happens if we add blue to the yellowto-green lines, red to the cyan-to-blue lines, and green to
the magenta-to-red lines? Subsequently, Fig. 5 is obtained.
Although Fig. 5 is brighter than Fig. 3 and Fig. 4 because
more colors are added, the image is still clearly visible [2].
Fig. 5 can be represented as spatial color mixing of cyan,
magenta, and yellow as the three primary colors. However,this does not imply that subtractive color mixing exists inspatial color mixing.

Fig. 5 This image is composed of lines of threecolors: white to cyan, white to magenta, and white toyellow.
3. SPATIAL COLOR MIXING ACCOMPANIED BY
COLOR ILLUSION
Fig. 4 was created by adding red, green, and blue colors
to Fig. 3. What happens when only green and blue areadded to Fig. 3? Precisely, we add green to the red line
and blue to the green line. Subsequently, Fig. 6 is obtained.
In this image, objects that were originally red appear to bereddish; however, red hues are no longer in the pixels as
the pixel colors are yellow to green, cyan to blue, or blue
to black. Red is represented by a combination of yellow,blue, and black. This phenomenon could be evaluated ascolor constancy; however, it can also be recognized as acolor illusion.

4. SPATIAL COLOR MIXING WITH TWO COLOR LINES
Thus far, three primary colors have been arranged in
independent lines. However, it is also possible to place two
primary colors in a single line. What happens when thegreen line and blue one in Fig. 3 are mixed into one line?
The mixed line includes green, blue, their mixed colors. Fig.
7 shows an example.

Fig. 7 This image is composed of lines of two colors:
red to black, and mixed colors of green and/or blue toblack.
5. SPATIAL COLOR MIXING WITH TWO COLOR LINESACCOMPANIED BY COLOR ILLUSION
What happens when green and blue are added to Fig.
7? More precisely, as the green and blue are added to the
red line, subsequently, Fig. 8 is obtained. In this image,objects that were originally red appear to be reddish;however, red hues are no longer in the pixels because
pixel colors are white to cyan or mixed colors of green
and/or blue to black. Red is represented by a combinationof white and black. Fig. 8 shows the two-color line
counterpart of Fig. 6.

Fig. 8 This image is composed of lines of two colors:
white to cyan, and mixed colors of green and/or blue
to black.
Fig. 6 This image is composed of lines of threecolors: yellow to green, cyan to blue, and blue toblack. Perceived red is illusory.

6. EXAMPLES OF THIS TYPE OF COLOR ILLUSION
Fig. 9 shows a demonstration, using a can of Coca-Cola,
which gained popularity on social networking sites in 2021.

Proceedings of 4th International Symposium for Color Science and Art 2023
The can appears reddish; however, the reddish section
consists of black and white stripes.

The examples of illusions shown thus far have been
based on photographic subjects and involve red objects.
This is because the effect is empirically convincing underthese conditions.
This effect can also be achieved using simple
illustrations rather than photographs. Fig. 11 shows anexample.

Fig. 11 The eye in the left image appears reddish andthat in the right appears to be bluish, though both arecomposed of black and white stripes.
This effect can also be observed in simpler images. Fig.
12 shows an example. The lower right circle that does notoverlap with other circles appears yellowish, although thearea is composed of black and white stripes.

Fig. 9 This Coca-Cola can appears reddish, though
the image is composed of black and white stripes.
In this example, it is common to suspect that the redcolor is due to our memory of the brand’s famous color;
however, this is not the case. To clarify this issue, we canuse another example. Observe Fig. 10. Not many people
would know about the previous JNR express colors.
In addition, as Fig. 10 is the counterpart of Fig. 2, thistechnique of painting red objects with black and white
stripes shows that it belongs to the phenomenon of color
contrast.

Fig. 12 The lower right circle that does not overlap
with other circles appears yellowish, though the area
is composed of black and white stripes.

Fig. 10 The window area of this train appears red, butthe color is composed of black and white stripes.

7. RELATION TO THE MUNKER ILLUSION
The Munker illusion is a phenomenon in which targets
are placed on a certain color background, and stripes ofanother color are placed on top of them. Color assimilation
is induced from the color of the stripes, and color contrast
is induced from the background [3, 4]. In Fig. 13, the redheart in the upper-left image appears magenta, while thatin the upper-right image appears orange. Moreover, theProceedings of 4th International Symposium for Color Science and Art 2023
green heart in the lower left image appears cyan, while thatin the lower right image appears yellowish green.

Fig. 13 The Munker illusion. The red heart appears
magenta (left) or orange (right). The green heart
appears to be cyan (left) or yellowish green (right).
The Munker illusion can be explained in the context of
spatial color mixing with two primary color lines. For
example, Fig. 14 is an image composed of lines of twocolors: one shows blue to black and the other displays
colors of red and/or green (including yellow hues) to black.
This image shows that magenta, the color of the lower
left portion of the circle that does not overlap with othercircles, is represented by a combination of red and blue
stripes. The background is composed of blue and yellow
stripes. These are consistent with the Munker illusion,
where the red heart appears magenta in the upper-leftimage of Fig. 13.
Fig. 14 also shows that cyan, which is painted in theupper portion of the circle that does not overlap with othercircles, is represented by a combination of green and blue
stripes. The background is composed of blue and yellow
stripes. These results are consistent with the Munker
illusion, where the green heart appears cyan in the lower
left image of Fig. 13.
In addition, the illusory yellow shown in Fig. 12 can also
be represented in the form of the Munker illusion in Fig. 15.

Fig. 14 The lower left portion of the circle that does
not overlap appears magenta, which is composed of
red and blue stripes. The upper portion of the circle
that does not overlap appears cyan, which iscomposed of green and blue stripes. The backgroundis composed of blue and yellow, and therefore hasthe same configurations as those of the Munker
illusion shown in the left two images of Fig. 13.

Fig. 15 The heart composed of black and white
stripes appears yellowish.
10. REFERENCES[1] A. Kitaoka, "Illusions based upon new types of spatial color mixing andapplication to VR," Keynote lecture, 26th Conference of the Virtual
Reality Society of Japan, Ritsumeikan University (online) (in Japanese)
http://www.psy.ritsumei.ac.jp/~akitaoka/VR2021.html (2021)[2] A. Kitaoka, "Spatial color mixing: an algorithm for subtractive colormixing with RGB as the primary colors and its application," The 2016
Summer Conference of the Vision Society of Japan, Toki Messe,

8. CONCLUSION
By investigating spatial color mixing, new color illusions
are found, and conventional color illusions can also be well
explained.

Niigata (in Japanese)
http://www.psy.ritsumei.ac.jp/~akitaoka/VSJ2016poster.doc (2016)[3] H. Munker, H, “Farbige Gitter, Abbildung auf der Netzhaut undübertragungstheoretische Beschreibung der Farbwahrnehmung”
Habilitationschrift, Ludwig-Maximilians-Universität München (1970)

9. ACKNOWLEDGMENT
This work was supported by JSPS KAKENHI, Grant
Numbers 15H01984 and 21H04426.

[4] D. Novick & A. Kitaoka, “The confetti illusion,” Journal of Illusion, 2,
https://doi.org/10.47691/joi.v2.6152 (2021)