## 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 and breaks I am taking the idea of the post “snowflakes“. There I used two copies of an image of six-fold rotational symmetry. One is rotated by 90 degrees. Putting both together I got an image with 12-fold rotational symmetry.

Now, to have an image of 4-fold rotational symmetry I simply take four copies of the original image.Three of them are rotated by 90, 180 or 270 degrees. Then four different pixels of the original image determine each pixel of the new image. I use them all in the same way to get a new image of four fold rotational symmetry.

I look at the three basic colors red, green and blue separately. Their values are between 0 and 255. To get much contrast I choose one of the four values from the original image. It is the value that has the largest difference to the middle at 127.

The resulting image is often too greyish. For more saturated colors I simply set the smallest of the three color components equal to zero and the largest equal to 255. Here are some typical results:

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