Showing posts with label bunny. Show all posts
Showing posts with label bunny. Show all posts

Sunday, January 18, 2009

Truchet Tilings

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Today I'm going to show a set of renders that are related to Truchet Tesellations. In 1704 Sebastien Truchet thought about a system of teselate a plane using oriented triangles. A modification of this one allow us to generate labyrinthic motifs using curved lines. In 1989 Pickover shown that it was an elegant method to see patterns in pseudorandom numbers secuences.

Seeing the Pickover's motifs I thought that it should be a way to tesselate a sphere without producing singularities at the poles.

So, here they are the ingredients:
  • Take a geodesic sphere discretized in triangles more or less regular with similar size.
  • Define 5 triangular tiles.
  • For each triangle replace it with one of the 5 tiles in a random fashion or with a certain probability distribution.
Here I show the results:

It can be shown only a certain kind of tiles:
Type 1

Type 2

Type 3

Type 4

Type 5

Only two types:




Uniform proability distributions:


Distributions of non uniform probability for each type:






Finaly all the types:


Images without the inner sphere:

and with a inner point of light:

With other materials:




Planar projections with non-linear cameras:


Finally, with all those projections depends on a triangular mesh it's possible to make denser motifs or even with a certain meshes. Like in this case, the Stanford Bunny: