Very pretty, and simple enough that I could show it to a kid. Also, it is a good thing that you didn’t use rectilinear co-ordinates in this, otherwise Descartes might have found it weird. Because ironically, he basically never used rectilinear co-ordinates. Instead, he just measured lengths along any two intersecting lines in whatever geometric construction he had.
Thanks for the kind words! It’s always fascinating to see how mathematicians of the past actually worked out their results, since it’s so often different from our current habits of thinking. Thinking about it, I could probably have also tried to make this accessible to the ancient Greeks by only using a ruler and compass—tools familiar to the ancients due to their practical use in, e.g. laying fences to keep horses within a property, etc.—to construct the Mandelbrot set, but ultimately….
I decided to put Descartes before the horse.
Very pretty, and simple enough that I could show it to a kid. Also, it is a good thing that you didn’t use rectilinear co-ordinates in this, otherwise Descartes might have found it weird. Because ironically, he basically never used rectilinear co-ordinates. Instead, he just measured lengths along any two intersecting lines in whatever geometric construction he had.
Thanks for the kind words! It’s always fascinating to see how mathematicians of the past actually worked out their results, since it’s so often different from our current habits of thinking. Thinking about it, I could probably have also tried to make this accessible to the ancient Greeks by only using a ruler and compass—tools familiar to the ancients due to their practical use in, e.g. laying fences to keep horses within a property, etc.—to construct the Mandelbrot set, but ultimately…. I decided to put Descartes before the horse.
(I’m so sorry)