< Fractals < Computer graphic techniques

3d still images

Converting 2D images to 3D

For height of each pixel one can use :

  • distance to boundary : "I'm using the distance estimate method (DEM) as the basis of my height values. (inverted, the log, scaled and streched, etc.)" Duncan C [1]
  • fractional iteration values [2]

video or animation made from 2D images

What is the difference between video and animation ?

Software used to do the conversion :

parameter plane

One can make videos using :

  • going along some paths on parameter plane ( for example internal and external rays )
  • Poincaré half-plane metric for zoom animation[4]
  • zoom into parameter plane[5][6][7] using automatic determination of Iteration Max number[8]
  • changing coloring scheme ( for example color cycling - Fractint)
  • changing some parameters of algorithm, for example :
    • maximal iteration of escape time algorithm
    • bailout value [9]

path

  • straight line from from c=-0.75+i to c=-0.75-i. It is mostly in the exterior of Mandelbrot set ( then Julia set is disconnected with no interior). There is only one point c=-0.75 where c belogs to the boundary of Mandelbrot set ( root point between period 1 and 2 hyperbolic components). In that point Julia set has interior ( parabolic ).[10]
  • from c=-2 to c=1.65 ( real slice of Mandelbrot set ) [11]
  • around a circle centred at -1 and with a radius of 0.25
  • around main cardioid [12]
  • parameter traces a circle centred at -0.29848658+0.65843271i and with a radius of 0.004. On the parameter plane, this does a circle around a point of the Mandelbrot fractal that is radiating 11 strands in a very loose spiral.[13]
  • races a circle centred at -1.57621921451761 and with a radius of 3.6 x 10^-10. On the parameter plane, this does a circle around a minibrot at that location without passing through the minibrot itself.[14]

References

  1. ↑ Duncanc Champney at fractalforums
  2. ↑ 3D plot with fractional iteration values by Duncan Champney
  3. ↑ answer on fractal forum
  4. ↑ Poincaré half-plane metric for zoom animation by Claude Heiland-Allen
  5. ↑ Really Deep Fractal Zoom Movie – Much Faster by Bruce Dawson
  6. ↑ Making Mandelbrot Set Movies by Tony Finch
  7. ↑ MLbrot by Daniel de Rauglaud
  8. ↑ Discussion : A way to determine the ideal number of maximum iterations for an arbitrary zoom level in a Mandelbrot fractal
  9. ↑ Gif image by jgabase : a wormhole effect on your fractals by changing the bailout dynamicaly
  10. ↑ Video : "Julia fractal morph: -0.75+i to -0.75-i" on youtube by rrwick
  11. ↑ video on youtube by rrwick
  12. ↑ video on youtube by rrwick
  13. ↑ video on youtube by rrwick
  14. ↑ video on youtube by rrwick
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