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:

yellowBlue1

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:

yellowBlue2

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:

yellowBlue3

Finally, the triangle wave makes:

yellowBlueTriangle

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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