The above animation is produced by Omega CAS Explorer:
A complex number can be plotted in a complex plain where the coordinate is the real axis and the coordinate the imaginary.
Let’s consider the following iteration:
where are complex numbers.
If (1) are started at for various values of and plotted in c-space, we have the Mandelbrot set:
When is held fixed and points generated by (1) are plotted in z-space, the result is the Julia set:
Let’s have a cow first:
There are more:
Drawing fractal by hand is tedious at best and close to impossible at worst. With the help of a CAS program, all you need is a few lines of code with a for-loop operation.
The fractal structure in Fig. 1 is generated from Gumnowski-Mira chaos model
Replace the term by with b = 0.9998, the result is shown in Fig. 2.
The fantastic fire bird fractal above is produced by Omega CAS Explorer: