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Category Archives: Cellular automata
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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a general parity rule and another example
To find the future state of a cell we choose some cells around the cell. This may include the cell itself. Then we calculate the sum of the states of these cells. If it is odd, the cell will have … Continue reading
Posted in Cellular automata, Fractals
Tagged Cellular automaton, Sierpinsky triangle
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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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The parity rule on a hexagonal lattice
The MIT group of E. Fredkin, N. Margolus, T. Toffoli and G.Y. Vichniac has studied many cellular automata on the square lattice. We can use their ideas as recipes to run on the hexagonal lattice. Particularly simple is the parity … Continue reading
Hexagonal cellular automata
Earlier I used a complicated cellular automaton to create images of snowflakes, see “Fake snowflakes“. It is based on a hexagonal grid in contrast to the wellknown cellular automata such as Conway’s game of life, that use square grids. Here … Continue reading
broken ornaments
Too perfect symmetry may become boring. If you have seen onequarter of an Ornament of fourfold rotational symmetry you have seen it all. Thus I wanted to break the symmetry and I programmed the computer to make mistakes. At each … Continue reading
Posted in Cellular automata
Tagged Cellular automaton, generative design, Rotational symmetry
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rainbow flakes
Snowflakes cannot make rainbows, but what would it look like if they could. That’s not science – that’s fiction, based on a modified cellular automaton.
Posted in Cellular automata
Tagged Cellular automaton, generative design, snowflakes
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better snowflakes
The artificial snowflakes of my earlier post have several defects in comparison to real snowflakes. First, the arms split up into five arms. But for real snowflakes they mostly split up only into three arms. Second, the edges should be … Continue reading
ornaments of eightfold rotational symmetry
The square lattice of cells has eight directions to nearest neighbors. Four directions are vertical or horizontal and the other four go diagonally. Thus I tried to create ornaments of eightfold rotational symmetry with my modified cellular automaton and using … Continue reading
Posted in Cellular automata
Tagged Cellular automaton, generative design, Rotational symmetry, Selfsimilarity
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