Introducing 

Prezi AI.

Your new presentation assistant.

Refine, enhance, and tailor your content, source relevant images, and edit visuals quicker than ever before.

Loading…
Transcript

The End

Fractal Distribution

Our Fractal...

Bibliography

  • https://plus.maths.org/content/unveiling-mandelbrot-set
  • http://www.arifractal.com/technologies-applications/fractal-distribution
  • http://mathworld.wolfram.com/MandelbrotSet.html
  • http://math.bu.edu/DYSYS/chaos-game/node6.html
  • https://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_dimension
  • https://www.bowdoin.edu/~dfrancis/askanerd/mandelbrot/

...will be made with this bubble and its reflection.

Let's zoom out some more...

Iteration Equation

Z = Z^2 + C

The Mandelbrot Set

History of the Mandelbrot set

"Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line."

-Benoit B. Mandelbrot

Characteristics of General Fractals

Its parts have the same structure as the whole, except that they are at a different scale and may be deformed.

They form by iteration (repetition)

It contains distinct elements with varying scales and cover a large range.

They have fractal dimension.

The Mandelbrot Set

Its form is extremely irregular and remains so.

What is a fractal?

A fractal is a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole.

Dimensional Specifications

N=r^D

The Process of Iterations

The Mandelbrot set consists of all of those (complex) c-values for which the corresponding orbit of 0 under x2 + c does not escape to infinity.

Learn more about creating dynamic, engaging presentations with Prezi