I haven’t had much time to play with the crossing lines. I do like their simplicity and the way they can create complex crossing relationships. I’ll be playing around with braids next, and integrating differential equations and chaos of course.

## Twist again – more geometric generative op art

## Askew Op Art Disk – Where’d the symmetry go?

The same equations were used to generate this image as well. Â The only difference is the starting point. Â Instead of expanding from the center of the distortion field, the starting point is displaced a little bit towards the bottom. Â This highlights a number of different things. First while the equations areÂ symmetric, the resulting image is decidedly asymmetric. Â If you follow the lines to the right vs. the ones to the left, you can see that the paths have decidedly different curves.

## 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.

## Twist #3

Double twist and wrap. Â While the last image was on the lackluster side, this one has everything turned up to 11. Â There is a strong deflection as the particles pass through the first peak and then they are swung back again as they exit the ring on the other side. Â An important thing to notice is that these are clearly defined and there is little mixing. Â If these equations were chaotic, then there would be mixing among the lines.

## Twist #2

## Simple twist

This shows the distortion in flow from a simple annular distortion. Â It’s part of a series that started with “distortion” and “a single twist and spray“

## A single twist and spray

One of the most popular images I’ve developed (I’ve no idea what verb to stick here) is this basic geometric op art style piece. Â I was just using a very simple mask to test out using differential equations to generate families of curves. Â It’s grown on me, and I’m starting to put some more images together in a similar style. Â This is the first of what I hope is a very fruitful series.

The first images I generated used first order differential equations, which have the nice property that the curves never cross. Â However, it severely limits the shapes that can be produced as each point has one and only one direction through it. Â Bumping up to second order added multiple directions through a point as an option, and it turns out some of those crossings can end up looking pretty sharp.