So why all these images? Beyond a casual interest in nonlinear systems, I use fractals as toy problems for exploring the performance of compute platforms.
They provide a variety of challenges to demonstrate:

• Single-thread performance
• Parallel performance
• Interprocess communication
• Memory system performance
• Impact of code branches
• Numerical precision

My early fractals were programmed on a MOS 6502 in assembly language. This device lacked floating point and a multiply instruction, which made it a challenging starting point - especially for transcendental functions. Over the years, these tests transitioned to Intel 8086, 8087, MMX, SSE, SSE2, AVX, and AVX2 (sadly, I've not been able to use AVX512).

GPU compute has afforded a 10-100x performance improvement in my personal experimentation in this area, especially for algorithms which are easily parallelized. Even for those which are single-threaded by nature, the abilty to avoid transferring a computed image across a bus to the video hardware can significantly speed up the process.

Of course there are challenges to GPU compute as well.

• Complexity of using the platform, unless simplifying with PyTorch, CUDA, or similar
• Poor performance of double-precision floating point numbers
• Hybrid techniques / interventions needed to incorporate double-precision (e.g. offload to CPU threads)

So my general approach is to create a plug-in architecture that generates images at "interactive" frame rates, usually 10-60 per second. This limits options for artistic treatment of the images, and thus they are rather plain. This approach does lend itself to making videos, so that's generally where I spend my time. After all, it is the dynamics of these systems that are interesting (at least to me) so video works well.