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.