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Monthly Archives: February 2013
Fractal surprise from complex function iteration: The movie
The movie shows the images as discussed int the earlier post “Fractal surprise from complex function iteration” for a decreasing value of the constant c. The program of the last post creates the movie frames. The movie begins with c=0.4 … Continue reading
Posted in Self-similarity
Tagged Chaos and Fractals, fractal, fractal design, julia set, Mandelbrot set, Self-similarity
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Fractal surprise from complex function iteration: The code
// here is the program for the last post // Fractal surprise from complex function iteration // simply use it in processing 1.5 (I don’t know if it works in the new version 2.) // you can download it from … Continue reading
Fractal surprise from complex function iteration
Recently I got the inexpensive Dover reprint of Clifford A. Pickover’s book “Computers, Patterns, Chaos and Beauty”. Part of it extends topics presented in “The Armchair Universe” by Dewdney. And there are other interesting ideas in Pickover’s book. Get it, … Continue reading
Posted in Self-similarity
Tagged Color, fractal design, iteration, julia set, Mandelbrot set
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How to program an ideal kaleidoscope
I have always been fascinated by kaleidoscopes. But often the mirrors were not well aligned resulting in disappointing images. Thus created a virtual kaleidoscope on the computer. Then it is easy to have perfect mirrors and to try different geometries. … 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 upside-down 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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The Voronio diagram of quasiperiodic tilings
In the post “Beautifying the double grid” I have shown how to get an interesting trellis by distorting the grid of a quasiperiodic tiling. Here I am showing Voronoi diagrams of the corner points of tilings, which make nice trellis … Continue reading
Posted in Tilings
Tagged Ammann–Beenker tiling, quasiperiodic Tiling, Socolar tiling, Stampfli tiling, Voronoi diagram
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Doubling the semiregular tesselation of hexagons and many triangles
There is one semiregular tessellation of six-fold rotational symmetry left over which I have not yet used to create a quasiperiodic tiling of 12-fold rotational symmetry. It has rings of triangles such that the hexagons do not touch each other, … Continue reading
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 4-fold rotational symmetry instead of 6-fold 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
Beautifying the double grid
The grids for quasiperiodic tilings do not look good because a lot of irregular shapes arise from superimposing two simple grids, see the article “Doubling the tessellation of triangles“. But we can distort these double grids and get new interesting … Continue reading
Posted in Tilings
Tagged Ammann–Beenker tiling, dual tesselation, Geometry, islamic art, quasiperiodic Tiling, Stampfli tiling
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