Tag Archives: Self-similarity

A fractal tiling of both octahedral and icosahedral symmetry

I want to show you a fractal tiling which can be seen as a decoration of a sphere with octahedral symmetry and at the same time as another decoration of a sphere with icosahedral symmetry. It arises as the limit … Continue reading

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Color symmetry using the length scale of the inflated lattice

I have shown some images with 2-color symmetry upon rotation shown in “images of 10-fold rotational …“. But the fast color changes they hacked them into small pieces. We can get better images if we use a color changing function with … Continue reading

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images with 5-fold symmetry and color change indicating self-similarity

And now for more images with 5-fold rotational symmetry and color change derived from self-similarity as discussed in “self-similarity and color modification“. Zoom in to see the molten watch faces in this image: Here I used the portrait of a … Continue reading

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Self-similarity and color modification

The Penrose tiling is self-similar as many other quasi-periodic tilings. It matches a copy of itself inflated by the golden ratio τ=(1+√5)/2≅1.618, see “Penrose tiling tied up in ribbons“. Noting that our quasi-periodic designs of 5-fold symmetry are closely related to … Continue reading

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Coloring the Julia set

The Julia set of a function f(z) in the complex plane has all points z that remain finite upon iterations of the function. In the last posts I have used expanding functions to get fractal images from iteration, as discussed … Continue reading

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Hints for experiments

You can modify the code of the last post “self-similar fractals … – the code” to produce new images. A large value for the imaginary part of the constant c often destroys the mirror symmetry and gives a more dynamic … Continue reading

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self-similar fractals with rotational symmetry from function iteration

I was looking at my posts of march 2013 on complex function iterations, see in particular “fractal surprise from complex function iteration” and “self-similar images from iterated mappings of the plane“, and I got some new ideas I want to … Continue reading

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