Mandelbulbs: the search for a 3D Mandelbrot Fractal

Follow Tom on his journey to Delft in the Netherlands in his quest to find a 3D Mandelbrot Set, otherwise known as a 'Mandelbulb'.
We begin with a discussion of the definition of a fractal, with examples from the natural world, as well as generating our very own in the form of the Koch Snowflake - a shape with infinite perimeter, but finite area. We then define the 2D Mandelbrot Set and introduce the concept of the Hausdorff Dimension which can take non-integer values, as exemplified by the Sierpinski Carpet Fractal. After a brief diversion via the Coastline Paradox and Space-filling Curves, we move onto 3D fractals in the form of the Menger Sponge, before finally using the White-Nylander Formula to generate our 3D renderings of the Mandelbrot Set, otherwise known as Mandelbulbs.
Produced by Quark Media - Jamie Halliday and Joseph Brooks Shuttleworth
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Tom is an Early-Career Teaching and Outreach Fellow at St Edmund Hall at the University of Oxford: www.seh.ox.ac.uk/people/tom-c...
For more maths content check out Tom's website tomrocksmaths.com/
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Attribution:
Paramount Pictures. ANNIHILATION. UA-cam Movies. March 25, 2019.
• Annihilation
Mandelbulb renderings from mb3d.overwhale.com/
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