Enzymind Labs

A two symbol Serpinski gasket (below) is embodied in a system with a terminating rule (the second rule only refers to itself), like Boundary 2x2 3-symbol and Boundary 2x2 5-symbol L-systems.

This two symbol system can be extended to related systems with more than two symbols in several ways, by replacing the last rule with rules that are also Serpinski-like.

Matlab command:
>> imOut = L_System_tiling( 'Two_symbol_Serpinski', 8, 2, 1, 0, '', 0, [0 0; 0 1], [1 1; 1 1] );

Four symbol Serpinski gasket 1

In this system the later rules are rotations of the first rule, with the unique corner refering to the next rule in a four symbol cycle:

The Serpinski pattern recurrs, rotated at smaller scales and with a cycling color.

Matlab command:
>> imOut = L_System_tiling( ''Four_symbol_Serpinski_10', 10, 4, 1, 0, '', 0, [0 0; 0 1], [1 1; 2 1], [3 2; 2 2], [3 0; 3 3] );

Color cycling of Four symbol Serpinski gasket 1 (2.6 MB):

It would be straight-forward to extend this to an eight symbol 3-D "Serpinski tetrahedron".

Here's the same pattern with a static 4-color scheme suggested by Ted Bell. What 4 colors are best distinguished?