A journey through the formula...

This is a video showing the famous Mandelbrot-Set, with the quite simple formula "a(n+1) := a(n)^2 + c" where a and c are complex numbers (x+y*sqrt(-1)) or (x+yi).

Each of the images forming the animation was calculated by a program i wrote in object pascal. I then put them together in AE and added the text. The color is "original" and not altered in post processing. Orange represents a point in the complex number plane which does not diverge towards infinity as we calculate the recursive calculation a certain number of times. The more blue the point is, the faster it diverges.

In order to keep the details clear, the program has to rise the recursion depth as we fly deeper into the fractal. The result is 30 seconds rendertime per frame in the last few seconds of the flight - which is why i then aborted.
(Note that you have to assist the flight during calculation when you zoom to a place you don't know yet - if you let it alone too long, you might be staring at an orange screen after a few steps)

One of the fascinating things about fractals is that you can zoom to a place nobody has ever seen before - ever. Now that's Star Trek, isn't it?! :)

Hope you enjoyed it. Thank you for watching.

Category:

Film & Animation

Tags:

• mandelbrot
• set
• benoit
• mathematics
• math
• chaos
• theory
• formula
• fractal
• flight
• flythrough
• manu
• thecrossi
• crossi

[BlueAquaMarina]

Oh!! That is incredibly beautiful!! Almost magical!! Thank you my dear!!

[BRUMARTUBE]

Be kind with the machines.

[Canadanarchy]

Nicely done.

[smashingparadox]

awe, I was hoping the journey would last a little longer

[rasmusfribble]

Awesome. I believe it's mandatory for me to ask you what music you used...?

[escstrg1]

cool vid, i understand, that your machine hated you ;-)

[dieseldizzy]

I love this stuff