This is my first experiment with canvas. I was trying to build a better understanding of the geometric uses of Clifford algebras. This little snip-it shows some features of the Clifford triple product in 2 dimensional Euclidean space.
Archives for November 2012
Twist again – more geometric generative op art
After fighting all the overlapping issues with second order equations, I switched back to first order and hard coded a single focus point in the equations. Â With that change I was able to start doing some more predictable plots with the ring functions.
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Askew Op Art Disk – Where’d the symmetry go?
The same equations were used to generate this image as well.  The only difference is the starting point.  Instead of expanding from the center of the distortion field, the starting point is displaced a little bit towards the bottom.  This highlights a number of different things. First while the equations are symmetric, the resulting image is decidedly asymmetric.  If you follow the lines to the right vs. the ones to the left, you can see that the paths have decidedly different curves.
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Circling back to a dead end.
These renderings never really went anywhere. They show chaotic orbits around 3 fixed attractive potentials while varying a uniform magnetic field. There are some lovely sweeps and folds as the chaos unfolds. I also like the glowing effect as the orbits get tightly wrapped around the centers of attraction. There wasn’t much to this other than some pretty curves, however, I did realize how essential drag is in making interesting forms. I suppose adding flocking and some higher order terms would help in adding further visual interest.
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Spider web fractal
It’s a little late for Halloween, but spooky nonetheless.
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Simple Op Art disk
This is what you get if you take the parallel stream from the rest of the series and replace them with a circular spray from the center of the distortion. Â Everything gets bent uniformly when it hits the ring. Â Moving to second order equations gives you the freedom to have multiple directions from a single point like this without a singularity.