3D Mandelbrot Set

[zak]

can you believe that this picture is a plot of a 3D mandelbrot set !!:





look at those great images here( very big page with many links):
http://www.skytopia.com/project/fractal/mandelbulb.html
i hope i can find some complete algorithm to implement those 3d mandelbrot in thinbasic
look at the following image from a "3D Fractal Gallery" wich resembles a temple it is in the bottom of other page:
http://www.skytopia.com/project/fractal/mandelbrot.html




all in all the site is magnificent, look at the projects tab ; many goodies.
another ref is an article "Pandora's 3D box" in the great free math magazine :
http://plus.maths.org/latestnews/sep...ndex.html?nl=1

[kryton9]

Beautiful stuff Zak, thanks.

[sblank]

Hi Zak,

You might want to look up quaternion Julia sets... those are really beautiful 3D projections of 4D fractals using quaternions (4D analogs of the complex plane).

I have some C/OpenGL/GLUT code that draws a point cloud quaternion Julia set, including a 3D Mandelbrot set from quaternions. It looks a bit different from the picture you posted, but interesting nonetheless. I would be happy to post the C code here as an attachment if you are interested? The skeleton of the program is similar to the FreeBasic OpenGL/GLUT parametric equation/trackball rotation program I posted in the Wayne City High gaming forum. The difference is in the math and plotting the quaternion point clouds (and the fact that the code is in C...).

A thinBasic port would be fantastic!

Cheers,

Stan

[zak]

Hi Stan
yes of course, if i or other user can convert some C codes to thinbasic this will be fantastic. we will try.
thanks

[sblank]

Hi Zak,

I'm attaching a picture:

quat.jpg

As well as the FreeBasic program that created the picture. What you see above is a Quaternion Julia Set rendered as a display list. It was created by testing 100 million random points in a 4x4x4 box using quaternions in a fashion similar to the 2D Mandelbrot Set in my Python text. The above image has full trackball rotation using the mouse point (passive mode).

I translated the program from C to FreeBasic and noticed no degradation in either speed of calculation or in animation. The original C program was created from a skeleton (illiSkel.c) provided by my good friend Prof. George K. Francis (Mathematics) at the U of I. I provided the quaternion math, Mandelbrot, and half-set options in C and the entire translation to FreeBasic.

The exe file below has 25 million test points... so be patient while the calculations are being done

Cheers,

Stan

[zak]

Hi Stan
the 3d graphics is great especially the 3D mandel , thanks for this, it is a pleasure for the eyes, it is good you have enabled choosing julia or mandelbrot (mand = 1 in your freebasic code) i have enjoyed more by the 3d mandel ,have you tried iter=5, incr = 5 the figure is like the temple above. i have downloaded freebasic and tried your examples, and indeed it is a speedy language.
i have translated your code to thinbasic, but as always there is obstacles. in never exit the calcit function if the loop is approximately more than 30000, so i tried manualy to choose :
glBegin(%GL_POINTS)
For foo = 0 To 30000
instead of
for foo = 0 to 1000000*incr
now even after that when going to function doRender() it stop in line:
glMultMatrixf (VarPtr(aff(1)))
error: Expected a parameter passed BYREF but found something else.
aff(1) is the first from array to aff(16).
so here is my buggy program.
as a reference to using :
TBGL_NewList
....
TBGL_EndList
look at my post about biomorphs there is a usage for lists:
http://www.thinbasic.com/community/s...ctal-creatures
again thanks for enabling us to see some freebasic examples.

PS: be carefull if want to experiment with the more than :
For foo = 0 To 30000
and you want to exit by clicking "X", the thinbasic.exe will still swimming in the memory, the only way to end process: by ctrl-alt-del, it is a problem of all ms windows programs