Tag Archives: hexagonal lattice

Decorations of semi-regular 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 semi-regular tilings? Could we decorate them too using mirrors? This would give us … Continue reading

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tiling with rhombs of 12-fold rotational symmetry

If we use n=3 in “Dualization method for ten-fold rotational symmetry – the code” we get the well-known 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

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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

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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

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Basic parity rule – sample images

To get smoother images I first use Gauss-blur 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

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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

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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

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