Op Art and More 

These fractals are based on Julia sets, which are represented be the given formula. All computations are done in the complex number space, i.e. each number consists of a real part which is used on the horizontal axis and an imaginary part which is used on the vertical axis. For each real part all existing imaginary parts are computed and are shown as colored pixels. The axis were built by 500x500 pixels, i.e. by 250 000 pixels. The formula was used 250 000 times construct a single picture. 

The value of each pixel was computed by iteration. In the majority of cases 50 iterations were used to construct the videos. In some cases the number of iterations was changed during recording to receive more details. Up to 4000 iterations were adjusted, i.e. 4000 computations were necessary to receive the value of one pixel. In this case about one million iterations were used for one single picture.

The replay of a video used 25 single pictures per second, i.e. it was necessary to compute 1500 single pictures with more than 30 millions computations even by only 50 iterations. 

The result of an iteration shows whether the iteration runs against infinite or shows apparently stable values. The power of infinity is represented by different colors. From blue to green via yellow and red the infinity becomes weaker. Black shows stable values and represents the virtual Julia set. The colored areas are called Fatou sets. 

The values of the real and imaginary axis often begin from -2 to +2. For computing 8 byte floating-point numbers were used. The formulas use the complex variable "z" and the complex constant "c" to construct the plane geometry. In many cases the constant "c" was changed during recording. Hereby results a strong variability of the Julia Sets which might to appear as extreme high velocity.

Some of the formulas were adopted by the mathematician  Michael Becker others were internally developed.

Further hints for computing fractals:

computing of fractals