The Mandelbrot Set: An Astronomical Mathematical Marvel...

Imagine a vast, complex universe filled with galaxies, stars, and planets swirling in a cosmic dance. Now, zoom in and look closely at the intricate patterns and structures within each galaxy. What if I told you that these patterns and structures could be explained by a simple equation? Enter the Mandelbrot set, a fascinating mathematical concept discovered by Benoit Mandelbrot in the late 1970s.

At its core, the Mandelbrot set is formed by iteratively applying a simple equation to a complex number and checking if the result remains bounded or not. The result is a beautiful and intricate fractal pattern that appears to go on forever, displaying self-similarity at different scales. But how does this relate to astronomy? Well, it turns out that the Mandelbrot set's mathematical properties have been used to model and analyze the complex structure of the universe, from individual galaxies to galaxy clusters.

This similarity is not just a coincidence but a reflection of the underlying laws of the universe. The Mandelbrot set, with its infinite complexity and beauty, serves as a metaphor for the patterns we observe in nature, from the branching of trees to the formation of coastlines. In this video, we will take a journey through the basics of the Mandelbrot set and its connection to astronomy. We will explore how the set's mathematical properties have been used to understand the structure of the universe, from the smallest galaxies to the largest clusters.

0:00 Introduction
2:08 The Beginning of Mandelbrot
5:38 The Math of Mandelbrot
9:05 The Astronomy of Mandelbrot

Thank you for watching.

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[ares]

is this channel still active? it's been like a month since a new video was posted and I actually really enjoy their videos

[nightwolf]

What happend to this channel? it was one of my favs was very interesting and informative easy to follow and loved her "robotic" voice...hope it comes back.

[SmurfsOMalley]

Is the channel still alive? Hopefully youre able to come back to it?

[Total_Entropy]

LOVE how they keep experimenting between narrators between different vids... ALL end up being ridiculous 😂😂😂

[thomasolson]

Everything you can do on the complex plane you can do with the regular x y plane. There is absolutely nothing special about the complex plane in this particular context. You just don't understand the geometry at play. To get the algebra that you need for this you gotta use the rotation matrix. (x+i*y)^n is a rotation about it self [1, 0].A^n. The Mandelbrot Set is a combination of vector addition and a rotation. You can rotate the recursive part to btw. You can get stars and other shapes if you do it right. That being said, there is probably a cycloid type thing that looks like a star.