Thank you for these- I saw the 1st, now I jumped to the last (’cause this is an intro course): and I’m _really_ impressed by the graphic work done here. I’m used to speedier presentations but he takes it slow and easy.
Seeing bifucation diagrams with the lorenz plots in this way is really nice: I remember playing with these using FRACTINT for DOS in 89->early 90s and it brings back memories of making my poor 286 do all of these calculations, making little changes to initial parameters and watching the results. I barely knew what I was doing but it didn’t matter: I loved how the tiniest little change could result in massive differences in the final results.
There’s beauty in imperfection. Found ancient fractal program I used in the late 80s/early 90s called FRACTINT. I remember spending a lot of time changing the parameters, making new fractals, zooming in, watching the colors come from the deepest calculable depths and exploding into life….and starting big and watching the colors go down into the depths of the fractals, to continue their lives, sight unseen by me, but I knew, mathematically, they _could_ still be there.
Yet, as beautiful and perfect as it is, I enjoy when things get even more complicated than that. What’s the calculation for this? A video taken of a fractal that was moving around, frames removed, the imperfect 256 colors reduced to a standard 256, resulting in different colors altogether… and a transparency that suddenly asserts itself in a bright FLASH every loop.
What’s that formula? That’s when things get interesting to me, for as perfect as our calculations may be, entering reality gets to be a little more complicated, and that intersection between perfected ideals (no matter how complicated) and actual complicated reality (no matter how simple) is an unending source of fascination to me.