Monthly Archives: June 2012

Snowflakes

I love the photographs of snowflakes by W. A. Bentley. From Dover Publications you can get a CD-rom with more than 500 pictures scanned in and ready to use on your computer. This is fantastic. As it is quite hot … Continue reading

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Blending tilings

Using semitransparent color to superpose tilings does not work out well because it is too difficult to control. Now I have a better idea. Simply draw the tilings as before. Then blend the pictures pixel by pixel by interpolating their … Continue reading

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Crazy graph paper

Here I am using the same morphing of the Ammann-Beenker tiling as in my earlier post “Morphing the Ammann-Beenker tiling“. Thus we see at the top a square grid, in the middle the Ammann-Beenker tiling and at the bottom a … Continue reading

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Morphing the tiling of octagons and squares in space

An animated morphing of quasiperiodic tilings passes perhaps too rapidly. As tilings repeat throughout space it is quite natural to show their morphing depending on the position in  space or on the computer screen. This we can examine more easily. … Continue reading

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Varying iteration

The number of iterations needs not to be a fixed number. It may vary depending on the position in the screen. This can show how iteration progresses, such as in this example: Here I used the iteration method of my … Continue reading

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Fooling around

Being tired from gardening and a long day out in the sun I made same programming mistakes and experiments. Thus I found that the iteration methods for quasiperiodic tilings can too be used to create mandala or rose windows. To … Continue reading

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Morphing the tiling of octagons and squares – a new twist

In an earlier post I have shown how the tiling of octagons and squares  transforms to the Ammann-Beenker tiling by using different lengths for the dual lines.  Here I am presenting another modification of the dualization method. The dual lines … Continue reading

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Morphing the Ammann-Beenker tiling

We can vary the dualization method in many ways. Here we play with the Ammann-Beenker tiling and use different lengths for the lines generated by the first square grid and the second square grid. This produces squares of different sizes … Continue reading

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Morphing the tiling of octagons and squares

In the last post “Doubling the tessellation of octagons and squares” I have used a grid of squares (in black) with diagonals (in blue). The blue lines are distinct and cannot be mapped onto the black lines by the symmetries … Continue reading

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Doubling the tessellation of octagons and squares

Regular octagons and squares make up a well-known semiregular tessellation that is often used to decorate floors Its dual grid is essentially a square grid with diagonal lines added. Four lines cross at the corner points giving the octagons of … Continue reading

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