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 Quasiperiodic design with 8fold rotational symmetry from 4dimensional space
 Rotational symmetry from space with an even number of dimensions
 Periodic design with 3fold rotational symmetry from 3dimensional space
 Inversion symmetry doubles the rotation symmetry for an odd number of dimensions
 quasiperiodic patterns of 5fold symmetry from 5 dimensional space
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Category Archives: Cellular automata
high resolution images with offscreen drawing
In an earlier post I have shown how to make smooth images at any scale using the pdfrenderer. But you can do this only with graphics objects such as line, point, shape, ellipse and so on. It won’t work if … Continue reading
Posted in Anamorphosis, Cellular automata, Extra, Fractals, Kaleidoscopes, programming
Tagged Geometry, image resolution, pixel, processing, programming, smoothing images
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Cellular automaton on quasiperiodic tiling
Any tiling can be used to define a cellular automaton. The tiles (squares, triangles, rhombs and other polygons) are simply the cells. Each tile has all other tiles with a common edge in its von Neumann neighborhood. I use the … Continue reading
cellular automaton on the semiregular tesselation of squares and octagons
For a change I am looking again at cellular automatons. The results using a square lattice were not really satisfying, see “cellular automaton with color on a square lattice“. There, horizontal and vertical lines dominated too much. To get different … Continue reading
Cellular automation on the lattice of triangles
The tessellation of triangles can easily be mapped onto the square lattice, see the figures at the left and right. Upright triangles (colored green) and upsidedown triangles (white) go into separate rows. The lines of interaction for the Von Neumann … Continue reading
Posted in Cellular automata
Tagged Cellular automaton, triangular lattice, Von Neumann neighborhood
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cellular automaton with color on a square lattice
I used the same methods as in the last post but now for a square lattice. I could not get similar results with 4fold rotational symmetry instead of 6fold rotational symmetry. Instead, the images were rather different. For my taste, … Continue reading
Posted in Cellular automata
Tagged Cellular automaton, Color, generative design, Moore neighborhood, square lattice
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Hexagonal cellular automaton in color
The images from the hexagonal cellular automaton shown in “Basic parity rule – sample images ” and “Modified parity rule – sample images ” are only black and white. But I prefer color. To get similar images in color I modified the … Continue reading
Modified parity rule – sample images
This is quite similar to the last posts with some small changes: As in the post “The modified parity rule” I am now counting the state of the cell itself too. To get a calmer image I am using gray as … Continue reading
Posted in Cellular automata
Tagged Cellular automaton, generative design, hexagonal lattice
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