Mandelbrot Set

[Johan Schoeman]

You need to read up on the Mandelbrot Set and then fiddle around with it. It is amazing....me thinks....use the link below play with it in your web browser. Zoom into some "insignificant" points and see how it repeats itself.

Mandelbrot Viewer

math.hws.edu

 

[derez]

[B4X] Mandelbrot Fractal

This code uses BitmapCreator class to create a Mandelbrot fractal: Sub CreateMandelbrotFractal As B4XBitmap Dim w As Int = bc.mWidth Dim h As Int = bc.mHeight Dim tx = FractalRect.Width, ty = FractalRect.Height As Double For row = 0 To w - 1 For col = 0 To h - 1...

www.b4x.com

 

[hatzisn]

You need to read up on the Mandelbrot Set and then fiddle around with it. It is amazing....me thinks....use the link below play with it in your web browser. Zoom into some "insignificant" points and see how it repeats itself.

Mandelbrot Viewer

math.hws.edu

View attachment 143617

I suppose that as Einstein was saying it is not a dice game by God. I've met the Mandelbrot set from the YouTube channel numberphile. The fact that this shape repeats itself the more you zoom in the complex numbers plane it does not sound like a coincidence to me (regardless of rotations).

 

[ac9ts]

I remember running these sets on a HP 9920 (MC68000/128K RAM) at work. Set it up when you went home and the image was just finishing when you came in the next morning!

Edit: I forgot to add this was 1985 if you couldn't tell by the make of the computer.

 

[Johan Schoeman]

Here is a very nice example (kick starting this Github project from within B4J. You need the following:

1. Attached B4J project
2. Attached Jar (MandelbrotMCV.jar) - copy it to your B4J additional library folder
3. ffmpeg (jars) - download version 0.7.0 from HERE - extract the jars and copy them to your B4J additional library folder

Start the project. If you want to ZOOM in then use the right hand button of your mouse to select a rectangle/square to zoom into. Zoom as much as what you like (I have not had a crash thus far when zooming in multiple times.

Base Image:

Zoom into the region of the sea horses and elephants:

17 x zooms in a specific area:

Zooming into a different area:

One of the numerous Mandelbrot Sets found while zooming in multiple time.

Zoomed in about 25 time to get to this

It is astonishing that such a simple formula can create these pattern by feeding the answer of the last calc into the calc for the next values (complex numbers).