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Monthly Archives: January 2013
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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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