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@trippyfractalart
Times Tables, Mandelbrot and the Heart of Mathematics
A great exploration on the math and terminology behind the curves, bulbs, and cardioids within the Mandelbrot Set (and beyond).
From Matheloger: The good old times tables lead a very exciting secret life involving the infamous Mandelbrot set, the ubiquitous cardioid and a myriad of hidden beautiful patterns. Time for the Mathologer to go on a serious fact-finding mission.
Fractal Flowers and the Bloom of Fire
The Golden Ratio (Phi) is intimately connected with flowers, as well as with fractal geometry. You can see all three of them represented beautifully here in one of the most popular fractal flowers -- "The Bloom of Fire". It was entirely generated with fractal geometry using the program Apophysis, and is available on prints worldwide here on Redbubble and here on Society6.
There is a great video from Numberphile that goes over the connection between the Golden Ratio and flowers here on YouTube.
Photo Credit: "Bloom of Fire" by San Jaya Prime (Instagram)
The Mandelbrot Set and How It Works
I've included this one because of how well it quickly covers the foundations of the complex plane, as well as the detailing of how the Mandelbrot Set is commonly colored.
An informative video about the Mandelbrot set that explains the mathematics, then provides some thought-provoking sentiment.
The Only Video You Need to See on the Mandelbrot Set
The video makes the claim in the title, and for the most part it lives up to it. This is definitely a great starting point to build knowledge on the history and some of the early findings in fractal geometry.
A detailed map of the Mandelbrot Set, in a beautiful vintage style
Designed by Bill Tavis, the map "introduces and explains many of the core concepts", and all in an exquisite vintage style to support readability and navigation. It's available for purchase from here on the main site.
A similar map was also created and made available through curiosity box. You can see that map here on YouTube.
The Mandelbrot Set with Doctor Holly Krieger
Famously beautiful, the Mandelbrot Set is all about complex numbers. Featuring Dr Holly Krieger from MIT.
Easily one of the top videos ever made covering the Mandelbrot Set.
Hidden Structures of the Mandelbrot and Julia Sets
This is a more rare exploration of areas not normally explored within or without the Mandelbrot and Julia sets.
An exploration of the correlations between the Mandelbrot Set and the Julia Sets for z^2 + c. Followed by some flybys of the full Mandelbrot/Julia structures. Finally, an attempt to show the complete 4D Mandelbrot Set..with partial success.
What's so special about the Mandelbrot Set? (Numberphile)
Very important for fractal lovers, fractal artists, and fractal geometers. It might be basic, but it makes all the difference. 1, 0, and -1. Everything else is insanity.
Featuring Ben Sparks discussing the Mandelbrot Set (and Julia Sets).