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

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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

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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

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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

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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

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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 well-known cellular automata such as Conway’s game of life, that use square grids. Here … Continue reading

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broken ornaments

Too perfect symmetry may become boring. If you have seen one-quarter of an Ornament of four-fold 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

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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.

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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

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ornaments of eight-fold 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 eight-fold rotational symmetry with my modified cellular automaton and using … Continue reading

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