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Fractals

Description

This is a simple app made for generating, viewing and exploring various fractals. Currently base classes are implemented for escape-time fractals and newton fractals with a few predefined fractals:

  • Burning ship fractal
  • Mandelbrot set
  • Tricorn fractal
  • Three Julia sets
  • Five Newton fractals
  • One miscellaneous

Prerequisites

To compile this program you need OpenGL Mesa libraries, especially:

sudo apt-get install libglu1-mesa-dev mesa-common-dev

as well as Qt5 (I've tested this on version 5.12.8). Here's a comprehensive installation guide: https://doc.qt.io/qt-5/gettingstarted.html

Usage

You can change currently displayed fractal as well as the color palette with the drop-down lists on the left. Fractal exploration is mainly done using mouse:

  • Zoom-in/Zoom-out with the scroll wheel or with LB/RB
  • Center the fractal on the mouse with middle button

Some additional controls are:

  • Increase/decrease maximum iterations during computations with '+' and '-'
  • Increase/decrease minimum iterations during computations with '[' and ']'
  • Change the calulation domain with arrows: pressing an arrow expands domain in that direction. Pressing an arrow with Control key down does the reverse.

Adding new fractals

Adding new fractals with already implemented base class (currently these are escape-time and Newton fractals) is very simple. You just need to add a new entry in the fractal map in the fractalsSupplier.h file.

Adding new escape-time fractal

This fractal is created using base class EscapeTimeFractal

            {
                    "Your escape-time fractal name",
                    new EscapeTimeFractal([](complex<double> zn, double x, double y) {
                        return yourFunction(zn, x, y); // Should return z_{n+1}
                    })
            },

Adding new Newton fractal

This fractal is created using base class NewtonFractal

            {
                    "Your Newton fractal name",
                    new NewtonFractal([](complex<double> z) { return someComplexFunction(z); },
                                      [](complex<double> z) { return derivativeOfSomeComplexFunction(z); })
            },

Important notes

Currently this program is set to use 20 threads for calculations. If you find that to be too much or too little it can be changed in the constants.h file.