Monthly Archives: March 2013

Running in circles

Another way for getting images with rotational symmetry: Take several similar images and map them on a circular disk. Muybridge’s Animals in Motion and The Human Figure in Motion are interesting sources. You can buy them already scanned from Dover … Continue reading

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rotational symmetry from superposition

Its snowing outside and it looks more like winter than spring. In two days we will have daylight savings time – what a mockery. Let’s stay inside and work on some pictures. To get images of rotational symmetry without distortion … Continue reading

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anamorphosis with 6-fold rotational symmetry

Thinking of snowflakes I made anamorphic images with 6-fold rotational symmetry based on the 6th power of z=x+iy. But because of the strong distortions I could not get anything resembling the crystalline beauty of snowflakes. Instead I got somewhat amorphous … Continue reading

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Anamorphic images with rotational symmetry

In our garden we have some polished spheres made of stainless steel. I like to look at them and to see the distorted images of the surrounding. The straight lines of the house and tree trunks become graceful curves. Polished … Continue reading

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An iterative hexagonal kaleidoscope

We can use the geometry of the last post differently. Draw inside a hexagon two equal sided triangles with the same corners as the hexagon. Then the intersection between the triangles gives a new smaller hexagon. Repeating this we get … Continue reading

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A fractal kaleidoscope

– whatever that means. I got the idea from the exterior snowflake and the Koch snowflake. They both are fractal curves and are discussed in Wikipedia and Wolfram math world. But I slightly modified the iteration scheme. I start with … Continue reading

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Just another kaleidoscope

I extend the ideas of my recent post on quasiperiodic kaleidoscopes. We cut the picture plane into many triangles of varying size. Then, we take a small region of some image and get from it pieces that we copy into … Continue reading

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Doubling the tessellation of triangles and squares with two-fold rotational symmetry

This is rather for the completeness sake: The last semiregular tessellation I have not yet used to get a quasiperiodic tiling. It has squares and triangles, as has another tessellation with four-fold rotational symmetry, see “Doubling the tessellation of squares … Continue reading

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Quasiperiodic kaleidoscopes: further results

Doubling the tessellation of octagons and squares gives a quasiperiodic tiling of eight-fold rotational symmetry, which makes an interesting kaleidoscope. Here is a sample result: Finally, I want to show you a result using the quasiperiodic tiling that doubles the … Continue reading

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Quasiperiodic kaleidoscopes

As you can see from my earlier post “kaleidoscopic images with local rotational symmetry” you cannot get seemless images of eight-fold rotational symmetry with a kaleidoscope of mirrors. This is also the case for 12-fold rotational symmetry and for other … Continue reading

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