So I finally got the conformal maps code to work with some of the other functions and the results are quite interesting and strange. Not really what I expected to get. The transformed images vaugely resemble the ones in my math textbook but don't match them exactly.
So again, here's the original image for reference:
I then applied the transformation $w = z^3$ to the image.
The results are quite satisfactory. No surprises there.
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| $w = z^3$ transformation |
Next I tried $w = z + \frac{1}{z}$. I didn't really get what I expected ...
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| $w = z + \frac{1}{z}$ |
$w = log(z)$ looks like someone flattened the thing along the third dimension.
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| $w = log(z)$ |
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| Another version of $w = log(z)$ with the image in a different position. |
The results for $w = sin(z)$ and $w = e^{z}$ were just plain weird.
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| $w = sin(z)$ |
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| $w = e^z$ |
But my favourite one was the transform $w = tan(z)$
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| $w = tan(z)$ |
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| $w = tan(z)$ with the image in a different starting position |
A perfect example of mathematics creating art. They're not as good as fractals but they're still pretty good.
1 comment:
These are really spectacular! They remind me of the time when i used to play around with fractal software and edit them using photoshop. Speaking of fractals, z + (1/z) reminds me of the Mandelbrot set (the hollow heart shaped part I mean). Wonder if they are related.
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