This discussion highlights the fascination with mathematical concepts, particularly Euler's relation, the properties of the number 'e', and the Cantor Set. Participants shared personal experiences that led to epiphanies in understanding complex mathematical ideas, such as the relationship between exponential functions and the unit circle. The conversation also touched on brain teasers involving geometry and the surprising implications of seemingly simple mathematical manipulations.
PREREQUISITESMathematicians, educators, students, and anyone interested in deepening their understanding of advanced mathematical concepts and their real-world applications.
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.