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Deviation Actions
Description
A 2-D slice through a symmetry plane of the Thue-Morse sequence extended to 3-D. Seventh generation, 128x128x128.
This corresponds to the plane centered on, and orthogonal to, a long diagonal of the Thue-Morse cube.
Ted Bell showed me another way to make this pattern, with a triangular replacement system: it can be considered as the Thue-Morse sequence on a triangular tesselation.
The long range self-similar structure of the Thue-Morse pattern is more easily seen in this slice than in the 2-D square system's pattern. Notice the slightly lighter/darker trapezoids that repeat at different scales; it is a discrete similarity tiling.
Download for 1500 x 1300 px. version.
System and code. Modeled and rendered with MATLAB and Space Software, respectively.
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There are no restrictions on use of this image. Claiming to be the originator or owner, explicitly or implicitly, is bad karma. A link (if appropriate), a note to markdow30@gmail.com, and credit are appreciated but not required.
This corresponds to the plane centered on, and orthogonal to, a long diagonal of the Thue-Morse cube.
Ted Bell showed me another way to make this pattern, with a triangular replacement system: it can be considered as the Thue-Morse sequence on a triangular tesselation.
The long range self-similar structure of the Thue-Morse pattern is more easily seen in this slice than in the 2-D square system's pattern. Notice the slightly lighter/darker trapezoids that repeat at different scales; it is a discrete similarity tiling.
Download for 1500 x 1300 px. version.
System and code. Modeled and rendered with MATLAB and Space Software, respectively.
----------------------
There are no restrictions on use of this image. Claiming to be the originator or owner, explicitly or implicitly, is bad karma. A link (if appropriate), a note to markdow30@gmail.com, and credit are appreciated but not required.
Image size
1550x1352px 921.14 KB
Comments4
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hmm i guess some connection with the multinomial coeff