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 :

• answer on fractal forum^[3]
• commons help

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