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. I was just using a very simple mask to test out using differential equations to generate families of curves. It’s grown on me, and I’m starting to put some more images together in a similar style. This is the first of what I hope is a very fruitful series.
A single twist and spray
The first images I generated used first order differential equations, which have the nice property that the curves never cross. However, it severely limits the shapes that can be produced as each point has one and only one direction through it. 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.