Fractals Made from Shape Languages and Fancy Geometry

[Hextakis_Lander]

The shape languages are called "Shape Grammars"
The fancy geometry is called "Kisrhombille Tessellation"

You make languages out of shapes and then the shapes interact to create complex shapes, the whole process guided by code.

They're fractals. Infinite. And as customizable as code. It's a geometry programming technology.

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Here's an overview of the geometry.

https://github.com/johnalexandergreene/Geom_Kisrhombille/blob/master/README.md

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Here's a tool for making your own custom grammars (it's easy) and looking at pretty pictures.

https://github.com/johnalexandergreene/Forsythia/tree/master/app/grammarEditor

There's a README there. It provides a little overview and explains the UI. There's also a video walkthrough that shows you how to make a simple grammar.

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Here's the main project. Much pictures and videos. Fractal dive videos too.

http://www.fleen.org/

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Peruse the github repo for various demos and stuff.

[tit_toinou]

I. LOVE. It.

Huge potential.

There's so much I want to do. Feels like the perfect tiling of the plane.

Any idea how to bring this to 3D ?

Cheers

[claude]

for 3D it would have to be based on cubes, I don't know if the cubes can be subdivided in a way to get a second cubic honeycomb in another orientation (to make it interesting):

https://en.wikipedia.org/wiki/List_of_regular_polytopes_and_compounds#Tessellations_of_Euclidean_3-space


the 2D concept is related to the (more general, but no nice GUI editor) subdivision tiling concept:
http://tilings.math.uni-bielefeld.de/

I used one such tiling (Amman A3 iirc) in my 'mandulia' project: https://mathr.co.uk/blog/mandulia.html

[M Benesi]

That is cool! 

[tit_toinou]

So all theses fractals are based on the kisrhombille euclidian tiling. I looked into it, I actually liked it at first sight because it made me think of the Pinwheel tiling and its Pinwheel fractal.

Kisrhombille is a actually a rep-tile like thoses :


You take one right triangle with PI/3 and PI / 6 angles and divide into 3 others similar triangles and repeat at infinity to get the 3-6 kisrhombille tiling, no ?

What would be awesome is a way to represent points in a kishrombille tilings with p/q coordinates or something to avoid floating point, in order to create infinite precision zoomable vector art with it (maybe that's what you already did ! I don't understand everything yet )

[tit_toinou]

I confirm the reptile aspect of the tiling !
Here's the shader : https://www.shadertoy.com/view/lsXfDl 
I don't know how to create the tiling from any point on the plane yet, I can only create the tiling from a triangle with this technique