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snowshughes

Escher Spiral Tesselation

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I am wondering if anyone can give me some advice, I found this awesome article about remapping rectangular grids to a spiral based grid.

The article can be found here: https://isohedral.ca/escher-like-spiral-tilings/ and the part I am trying to recreate can be seen in the following Screenshot:
image.png.b59b27e010b2af08f2abe10d4d2c8bbc.png
 

I tried to implement the simplified version of this equation but the outcome looks nothing like the diagram above. If anyone could point me in the right direction it would be greatly appreciated.

image.thumb.png.415922c77bc9d0376609c5a2b45a730f.png 

Many thanks,

S

EscherSpiral-01.hiplc

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3 hours ago, Librarian said:

@snowshughes You have I think those ex on Berlin Math 2016 year or 2018 ...
Conformal Mappings
Mobius strip-..
here its files from I think 2018

 

Thanks so much for your help @Librarian but I couldn't find what I needed in your files. They will definitely be a useful reference for future projects though.

I only showed a single tile which is an error on my part. The idea is that once I nail the correct mapping from rectangular to spiral I would be able to carry out this mapping on a larger grid which would produce a large tiled spiral shape as shown in the attached image.

spiral_grid.png

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Posted (edited)

Hi,

here is an approach. The formula is similar to your example only the parameter space is bit different. One value should be between 0 and 2 Pi.

 

esher_spiral_mapping.hipnc

Edited by Aizatulin
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56 minutes ago, Aizatulin said:

Hi,

here is an approach. The formula is similar to your example only the parameter space is bit different. One value should be between 0 and 2 Pi.

 

esher_spiral_mapping.hipnc

@Aizatulin thanks you so much, this is exactly what I was looking for.

I also love the way you created the stripes with VEX, super slick.

  • Like 1

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