The discussion revolves around the fascination with mathematics, exploring various concepts, surprising results, and personal anecdotes related to mathematical ideas. Participants share their experiences with mathematical phenomena that they found intriguing or mind-blowing, touching on topics such as exponential functions, Euler's relation, Cantor's theorem, and brain teasers involving geometry.
Participants generally share a sense of wonder about mathematical concepts, but there are disagreements regarding the interpretation and significance of the brain teaser involving the string around the Earth. Some find it straightforward while others see it as more complex.
Some assumptions about the brain teaser, such as uniformity of the gap and the feasibility of folding paper multiple times, remain unresolved and are points of contention among participants.
Not wishing to cast aspersions upon these quite beautful works, but it seems to me, the real charm of Mandelbrot set and Julia sets is that they are entirely natural. This seems like the gilding of a pretty incredible lily.turbo-1 said:That is the "magic". You get to apply symmetries, inversions, etc to make your images. Most of the horsepower comes from choosing which functions you want to apply in each layer, where to set the transparency limits and how to implement those, and what color schemes and gradients to apply. You can of course recover Mandelbrot and Julia sets in their original iterations and make beautiful images playing with only palettes and gradation slopes, etc, but that is not really satisfying. As I noted in another post recently, my "take" on creativity has a decidedly technical bent.