The Hat Tiling

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I recently made up a few alternative colour palettes for Craig Kaplan's excellent Shadertoy applet, based on an idea by Labbé and Selinger.



The main advantage of the application, is that the user can venture out to far away places in an instant, by inputting X,Y coordinates under GLOBAL_TRANSLATION.  Changes to EDGE_THICKNESS of the hat, SCALE and TRANSLATION_SPEED of the animation, can be easily modified.  There's also SHIFT_SPEED that reorganises some tiles within a patch (it's quite spectacular).  Warning: input very small values between 0.01 and 0.05 for best results (https://www.shadertoy.com/view/s3lGD7)

The first set of eight colour palettes I created, were based on the numbering of hats from the paper (https://arxiv.org/pdf/2604.20964).  



Those to the right of the first image, use the same colours but have been exchanged:






All other colour palettes below, are based on my modified version of Labbé and Selinger's numbering system.  This is better for accentuating the "highways and junctions".




Here is an edited version of the original "rainbow" palette coupled with its "twin".  Colours are as the original but the order (or pairing) has changed:  



Images below use six colours:




Colour blindness friendly palettes:



Minimal colour schemes:



Various three and four colour combinations:





The last example utilises seven colours and its twin:



If you wish to try out some of these for yourself, simply copy and paste one of the TXT files that store the RGB values (link below) into the highlighted area of live code, then compile.

https://www.mediafire.com/folder/u8ybzsoejy9od/Shadertoy_hat_applet




Software used:

ColorBrewer: https://colorbrewer2.org/#type=sequential&scheme=BuGn&n=3

Paintshop Pro 7 (virtually obsolete; no link)

Irfanview: https://www.irfanview.com/

Arnaud Chéritat's Dedicated Tiling Applet:




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