Enzymind Labs

These 5 symbol L-systems have a "terminating" rule that refers only to itself. This often results in large contiguous regions, often with a thin fractal boundary. In these examples the boundary is labeled black and the final (fifth) terminating symbol is labeled white.

The algorithms are represented by a graphic which corresponds to this pseudocode:

{ start with a symbol or symbol array
repeat for n_g generations:
{ for each symbol apply the symbol's replacement rule }

replace each symbol with a motif (for these examples, either black or white)
}

Bound 2x2 5s 1:

High resolution Bound 2x2 5s 1 system pattern

This boundary is perfectly self similar (is fully composed of copies of itself) at scales that are powers of two. Note that the boundary's intersection with the edge divides the edge in fractions of the form n*(1/3)^m where n and m are integers.

Bound 2x2 5s 1 is a bounded fractal tiling composed of a single fractal prototile that occurs at two orthogonal orientations:

Matlab command:
>> imOut = L_system_tiling( 'Bound_2x2_5s_1', 11, 5, 1, 0, 'Bound_2x2_5s_1_motifs.png', 0, 'Bound_2x2_5s_1_rules.png' );
(see attached "motif" and "rule" argument files)

Bound 2x2 5s 1 tilings:

The following are equivalent to tilings of the Bound 2x2 5s 1 system pattern, although some are modeled as an L-system with a 2x2 array of initial symbols.

This system (and the next) is the same as a composite of four of the Bound 2x2 5s 1 pattern rotated sequentially around the 2x2 cycle.

High resolution Bound 2x2 5s 1_tiling 1 system pattern

Matlab command (see attached argument files):
>> nimOut = L_system_tiling( 'Bound_2x2_5s_tiling1_9', 9, 5, 1, [0 1; 2 3], 'Bound_2x2_5s_1_motifs.png', [0 1; 2 3], 'Bound_2x2_5s_1_rules.png' );
(see attached "motif" and "rule" argument files)

Matlab command:
>> nimOut = L_system_tiling( 'Bound_2x2_5s_tiling2_9', 9, 5, 1, 0, 'Bound_2x2_5s_1_motifs.png', [3 2; 1 0], 'Bound_2x2_5s_1_rules.png' );
(see attached "motif" and "rule" argument files)

Various tessellations of Bound 2x2 5s 1 (including those above) bound this second fractal prototile. The Bound 2x2 5s 1 prototile can be formed from unions of this tile and a scaled copy. Note that the "points" of a convex hull around this shape are not on a regular octagon; edges of alternating vertices of a bounding 8-sided figure describe different angles. [To Do: Illustrate straight boundaries and angles and 'darts'.]

Caterpillarillpretac:

Large versions

The Bound 2x2 5s 1 boundaries are combined, tiled and colored to form the Caterpillarillipretac image.

Mouse teeth weave:

Larger versions, up to 3500 x 3500 px.

This regular square tessellation (tiling) has a motif based on the largest linear features of the Bound 2x2 5s 1 boundary. See Mouse teeth weave description for construction details, templates, and related colorings.

Thirds waves:

Larger versions, up to 8000 x 1000 px

This is a coloring of a regular square tessellation with a motif that includes a recurrent similarity transformation. The motif basis pattern is derived from the largest linear features of the Bound 2x2 5s 1 boundary. See Thirds waves description for construction details and templates. The coloring is vaguely naturalistic, as ocean and atmosphere are suggested by the wave-like spiral elements.

[To Do: Add other examples.]

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