Warning

If your computer holds considerably less memory than 500 Mbytes or if its frequency is far below 1 GHz then you should not open these GIF-animations. Likewise if your internet connection is rather slow then think if you really want to call these files, since they really are huge - some 100 Mbytes.

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Making of animations

When I started drawing details from the borders of mandelbrot sets I came to the idea to start with a very detailed picture and then to enlarge it’s width by a constant factor; for every step a picture is saved to a file containing a sequential number starting with 000. The sequence ends when the enlargement becomes less than 1.0.

So for these files I started with a picture enlarged 10^16...10^17 times. It is saved to a file start.frc (this is a private format containing all the parameters to calculate the picture).

Then in a first session set the enlargement factor to fifth root of 10 (1.584893...) so output is roughly 80 pictures respectively five pictures per decade in enlargement. At lower enlargements pictures usually will not show too much pleasing details. So I look for the first picture where the story starts "running" - lets it be number 62, i.e. 62 / 5 or about 12.4 decades. The span between 1 and 12.4 * 10 ^ 10 shall be covered by 200 pictures, so 200 / 12.4 = 16.13 pics per decade. Enlargement factor from pic to pic is 16.13th root of 10 or 1.1534.

Creating an animation from those pictures is done with Gamani movgear.exe Ver. 4.2. This version offers the possibility to combine all these pictures (files) written to a separate directory by selecting them with Ctrl-A (all) and input them into the program file with a single click. Write this partial animation to a preliminary file, then invert the oder of the pics, remove the first and the last one, finally add the above preliminary file.

To end up speed of representation is set to 10 up to 12 pics/second and size from 1001x1001 to 700x700 - all within Movie Gear. This in the end gives the files presented here of some 100 Mb each.

Color tables

My system to create surfaces allows 256 different colors all defined in RGB-values. Colors 0 to 16 are reserved for elements of the program (buttons etc.), 255 is defined as white. For graphics there remain 238, to be defined per user-defined RGB-values.

238 colors for a Mandelbrot- or Julia-picture seems to be modest, but I think, it is enough.

Function Minimax

The functions, activated by pressing the button labeled "Minimax" do the following:
  1. In the computed picture the uppermost (max) and the lowest (min) color value is searched.
  2. The "graphic" colors 17 - 254 (defined in a table) are distributed evenly between min and max.

This has the effect to present sharpness of edges (e.g. of a secondary Mandelbrot set) more clearly.

However it is sage to calculate more precisely, i.e. to enlarge iteration numbers to get distinct edges before switching to Minimax.


Advantage of Minimax is to destibute colors at its best on every picture, disadvantage is when calculating series of pictures as e.g. for our animations colors occasionally may flicker.
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