fractal visualization

Submitted by mfg on Mon, 05/09/2016 - 18:58
English
The visualization of fractal structures is rather complicated due to the intricacy of the boundary of the confined sets.
zero c2i0E-1+2(-.1;-.1,0)(1.47;-1.7,.5)
ix set in the vicinity of zero c2i0S-1+2(-.1;-.1,0)(1.47;-1.7,.5)
  1. It is possible to visualize two dimensional intersection planes of the tridimensional structure. The bound set as well as escape velocities are shown.
  2. It is also possible to visualize the three dimensional structure in 2D via ray tracing algorithms.
  3. It would be interesting to explore the pseudo three dimensional visualization:
    1. projection in translucent planes.
    2. estereoscopic images - either with colour, polarization or dots superpositions.
  4. Also, to explore the tridimensional fractal structure via the generation of digital holograms.

We shall presently center in: visualizations of intersections with planes and visualization via ray tracing of the three dimensional structure.

visualization of intersection planes

In this case we use C to compile the recurrence relationships, the magnitude condition and the number of iterations for each point on the plane. Thereafter, the result is rendered with mathematica or a similar drawing programme.

visualization via ray tracing

It is essential to use open source programmes in order to be able to modify them. Furthermore, open source programmes, in addition to being free, they are a fair way of collaborating and advance in human knowledge.

Initially, the programme Gestaltlupe developed by Traffasel was used. Impressive images were obtained.

Very impressive images have also been obtained with the programme Mandelbulber developed by the project leader Krzysztof Marczak and the programmers Krzysztof Marczak, Sebastian Jennen, Graeme McLaren, Bernardo Martelli.