## 2 Methodology  
### Spiral Strip Design  
We start by defining the spiral with  
\[r=a+b\varphi^{\prime}/2\pi, \tag{1}\]  
where \(r\) represents the distance from the center of the polar coordinate system. \(\varphi^{\prime}\) is a variable with values between zero, representing the start of the spiral, and some maximal value, representing the spiral endpoint. The expression in Equation (1) represents an Archimedean spiral, since \(r\) increases linearly with \(\varphi^{\prime}\). An increase in \(\varphi^{\prime}\) for \(2\pi\) represents one spiral loop. \(a\) and \(b\) are two parameters, with \(a\) representing the distance of the spiral starting point from the center, and \(b\) the radial distance between consecutive loops of the spiral (Figure 1a). In the Cartesian coordinate system, the spiral curve can be expressed as  
\[x = r\cos\left(\varphi^{\prime}+\varphi_{0}\right), \tag{2}\] \[y = r\sin\left(\varphi^{\prime}+\varphi_{0}\right), \tag{3}\]  
with \(\varphi_{0}\) being an additional parameter representing the angle between the \(x\) axis and line that links the center, and the spiral staring point (Figure 1a). A small change in \(\varphi^{\prime}\), which we denote as \(\mathrm{d}\varphi^{\prime}\), causes small changes in the \(x\) and \(y\) coordinates. These changes can be expressed from Equations (2) and (3) with the use of total derivatives, which yields  
\[\mathrm{d}x =\frac{b\cos(\varphi^{\prime}+\varphi_{0})-(2\pi a+b\varphi^{ \prime})\sin(\varphi^{\prime}+\varphi_{0})}{2\pi}\mathrm{d}\varphi^{\prime}, \tag{4}\] \[\mathrm{d}y =\frac{b\sin(\varphi^{\prime}+\varphi_{0})+(2\pi a+b\varphi^{ \prime})\cos(\varphi^{\prime}+\varphi_{0})}{2\pi}\mathrm{d}\varphi^{\prime}. \tag{5}\]  
The length of a small spiral segment \(\mathrm{d}l\) that corresponds to \(\mathrm{d}\varphi^{\prime}\) can be expressed as  
\[\mathrm{d}l=\sqrt{\mathrm{d}x^{2}+\mathrm{d}y^{2}}=\mathrm{d}\varphi^{\prime} \sqrt{a^{2}+\frac{ab\varphi^{\prime}}{\pi}+\frac{b^{2}(\varphi^{\prime 2}+1)}{4\pi^{2}}} \tag{6}\]  
This equation can be reversed to obtain the change in \(\varphi^{\prime}\) if one would move a short distance along the spiral (represented by \(\mathrm{d}l\))  
\[\mathrm{d}\varphi^{\prime}=\mathrm{d}l\left(a^{2}+\frac{ab\varphi^{\prime}}{ \pi}+\frac{b^{2}\big{(}\varphi^{\prime 2}+1\big{)}}{4\pi^{2}}\right)^{-\frac{1}{2}} \tag{7}\]  
The polar coordinate system can be used to define the geometric shapes of individual segments. In this case, the two straight borders of each segment can be parallel with the \(r\) axis of the polar coordinate system, while the two other curved borders can be along Archimedean spirals. However, the visual inspection of such spiral strips highlighted some problems--the segments can look deformed, especially near the center of the spiral, and the result is less visually appealing. This prompted us to define a new coordinate system where one axis is always parallel to the spiral curve while the other is always perpendicular. The segments looked less deformed in the new coordinate system, and the result was more visually appealing. A comparison of results from both coordinate systems is available in the Supplementary Materials. Figure 1: Design of the spiral strip graphic. (**a**) Spiral curve (thick line) defined by Equations (2) and (3) shown in a Cartesian coordinate system denoted by the \(x\) and \(y\) axes. Dashed circles represent the distance to the center of the coordinate system. (**b**) Similar to (**a**), but with individual segments shown along the spiral. The segment’s width is denoted by \(w\) and the length by \(l\). The inset area in the middle shows a more detailed view of the region denoted by the square. The custom coordinate system can be represented by a set of two basis vectors that change along the spiral. The basis vector that points along the spiral curve (\(\mathbf{e}_{l}\)) can be expressed as  
\[\mathbf{e}_{l}=\frac{1}{\mathrm{d}l}\binom{\mathrm{d}x}{\mathrm{d}y}=