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Tag Archives: hexagonal lattice
Decorations of semiregular tessellations
In the last posts I have shown kaleidoscopes that make repeating images in Euclidean, spherical and hyperbolic spaces. They are decorations of regular tilings. But what about semiregular tilings? Could we decorate them too using mirrors? This would give us … Continue reading
Posted in Kaleidoscopes, Tilings
Tagged hexagonal lattice, kaleidoscope, mirror symmetry, Tessellation
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tiling with rhombs of 12fold rotational symmetry
If we use n=3 in “Dualization method for tenfold rotational symmetry – the code” we get the wellknown periodic tiling with rhombs of 60 degree acute angle and hexagonal symmetry. It is useful for isometric projections, see the geometricon.wordpress.com blog … Continue reading
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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Basic parity rule – sample images
To get smoother images I first use Gaussblur and then a threshold filter. Here I am showing results for the parity rule on the hexagonal lattice with the von Neumann neighborhood. You get more details in my earlier post “The … Continue reading
Imitating snowflakes with a simple cellular automation
In an earlier post “Fake snowflakes” I already created images that resemble snowflakes. I used a rather complicated method. Now I have found a much simpler cellular automaton that gives similar results. Again I use a hexagonal lattice. Each cell … Continue reading
Posted in Cellular automata
Tagged Cellular automaton, generative design, hexagonal lattice, Snowflake
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Further images from hexagonal cellular automatons
I continue to pursue my main interest – to create geometric images. Thus I have tried new recipes for cellular automatons on the hexagonal lattice. The cells have either state 1 or 0. To get symmetric images we start with … Continue reading
Posted in Cellular automata, Fractals
Tagged Cellular automaton, fractal, hexagonal lattice
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Conway’s game of life on a hexagonal lattice
Out of curiosity I searched for a similar cellular automaton as Conway’s game of life on a hexagonal lattice. It should have gliders and use the Moore neighborhood as defined in the earlier post “hexagonal cellular automata“. I found gliders … Continue reading
Posted in Cellular automata
Tagged Cellular automaton, Conway's game of life, glider, hexagonal lattice
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The modified parity rule
A small change of the parity rule gives us new interesting images. In addition to the states of the six nearest neighbors of a cell we count the state of the cell itself too. The cell has state =1 in … Continue reading
Posted in Cellular automata, Fractals
Tagged Cellular automaton, fractal, hexagonal lattice, Selfsimilarity
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parity rule – the video
In the last post I did not do a good description how the cellular automaton with parity rule evolves on a hexagonal lattice. Thus I made a video using the von Neumann neighborhood. You can see reappearing inflating generations with … Continue reading
Posted in Cellular automata
Tagged Cellular automaton, fractal, hexagonal lattice, Selfsimilarity, square lattice
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