Five fold rotational symmetry: Tuning the harmonics

In “better images from higher harmonics ?” I have replaced the basic sine and cosine functions by Fourier series approaching a symmetric triangular wave. This gave images with more details and somewhat smaller bulls-eyes. Here I want to show similar results for an image with 5-fold rotational symmetry using a different input image.

With only the basic sine and cosine waves I get:


The center of perfect 5-fold rotational symmetry lies slightly at the right of the center of the image. Note the concentric shapes inside a pentagon and the large orange bulls-eyes.

Adding the third harmonic I get more details:


At the center we now have star like shapes instead of the pentagon and the circle.

Using the basic wave together with the third and the fifth harmonics gives smaller changes:


Finally, the triangle wave makes:


Now, straight line segments appear. The image has a more crystalline appearance. The rather large orange blobs remain, but they have now a more interesting polygon shape.

I like that I can tune the images changing the wave function, but I am disappointed that the large blobs do not disappear.


This entry was posted in Anamorphosis, Kaleidoscopes, programming, Quasiperiodic design and tagged , , . Bookmark the permalink.

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