This video explains the Feigenbaum constant very well.
A program was written which represents the Feigenbaum constant. In addition to that, there is also a Mandelbrot set.
What is a Feigenbaum constant?
In mathematics, specifically bifurcation theory, the Feigenbaum constants are two mathematical constants which both express ratios in a >bifurcation diagram for a non-linear map. They are named after the physicist Mitchell J. Feigenbaum.
What is a Mandelbrot Set?
Images of the Mandelbrot set exhibit an elaborate and infinitely complicated boundary that reveals progressively ever-finer recursive detail at increasing magnifications, making the boundary of the Mandelbrot set a fractal curve. The "style" of this repeating detail depends on the region of the set being examined. Mandelbrot set images may be created by sampling the complex numbers and testing, for each sample point {\displaystyle c}c, whether the sequence {\displaystyle f_{c}(0),f_{c}(f_{c}(0)),\dotsc }{\displaystyle f_{c}(0),f_{c}(f_{c}(0)),\dotsc } goes to infinity. Treating the real and imaginary parts of {\displaystyle c}c as image coordinates on the complex plane, pixels may then be coloured according to how soon the sequence {\displaystyle |f_{c}(0)|,|f_{c}(f_{c}(0))|,\dotsc }{\displaystyle |f_{c}(0)|,|f_{c}(f_{c}(0))|,\dotsc } crosses an arbitrarily chosen threshold. If {\displaystyle c}c is held constant and the initial value of {\displaystyle z}z is varied instead, one obtains the corresponding Julia set for the point {\displaystyle c}c.
Look:
Prerequisites:
- At least >=QT 5.14.0
How to compile:
If you have the QT Creator installed, than this will be a piece of cake. All you have to do is to double click on KomplexeZahlen.pro and you are good to go.