4th Order ABS Mandelbrot Variations (Complete Set) by Kosmic-Stardust

4th Order ABS Mandelbrot Variations (Complete Set)


***Non ABS Variations (2)


Mandelbrot 4th Order:
        zi = 4 * zr * zi * (zrsqr - zisqr) + JuliaI;
        zr = zrsqr * zrsqr + zisqr * zisqr - 6 * zrsqr * zisqr +JuliaR;
        zisqr = zi * zi;
        zrsqr = zr * zr;

Mandelbar 4th:
        zi = -4 * zr * zi * (zrsqr - zisqr) + JuliaI;
        zr = zrsqr * zrsqr + zisqr * zisqr - 6 * zrsqr * zisqr +JuliaR;
        zisqr = zi * zi;
        zrsqr = zr * zr;


***Straight ABS Variations (16)


Burning Ship 4th:
        zi = 4 * abs(zr * zi) * (zrsqr - zisqr) + JuliaI;
        zr = zrsqr * zrsqr + zisqr * zisqr - 6 * zrsqr * zisqr +JuliaR;
        zisqr = zi * zi;
        zrsqr = zr * zr;

Burning Ship 4th Partial Imag:
        zi = 4 * zr * abs(zi) * (zrsqr - zisqr) + JuliaI;
        zr = zrsqr * zrsqr + zisqr * zisqr - 6 * zrsqr * zisqr +JuliaR;
        zisqr = zi * zi;
        zrsqr = zr * zr;

Burning Ship 4th Partial Real:
        zi = 4 * abs(zr) * zi * (zrsqr - zisqr) + JuliaI;
        zr = zrsqr * zrsqr + zisqr * zisqr - 6 * zrsqr * zisqr +JuliaR;
        zisqr = zi * zi;
        zrsqr = zr * zr;

Burning Ship 4th Partial Real Mbar:
        zi = -4 * abs(zr) * zi * (zrsqr - zisqr) + JuliaI;
        zr = zrsqr * zrsqr + zisqr * zisqr - 6 * zrsqr * zisqr +JuliaR;
        zisqr = zi * zi;
        zrsqr = zr * zr;

Celtic Burning Ship 4th:
        zi = 4 * abs(zr * zi) * (zrsqr - zisqr) + JuliaI;
        zr = abs(zrsqr * zrsqr + zisqr * zisqr - 6 * zrsqr * zisqr) +JuliaR;
        zisqr = zi * zi;
        zrsqr = zr * zr;

Celtic Burning Ship 4th Partial Imag:
        zi = 4 * zr * abs(zi) * (zrsqr - zisqr) + JuliaI;
        zr = abs(zrsqr * zrsqr + zisqr * zisqr - 6 * zrsqr * zisqr) +JuliaR;
        zisqr = zi * zi;
        zrsqr = zr * zr;

Celtic Burning Ship 4th Partial Real:
        zi = 4 * abs(zr) * zi * (zrsqr - zisqr) + JuliaI;
        zr = abs(zrsqr * zrsqr + zisqr * zisqr - 6 * zrsqr * zisqr) +JuliaR;
        zisqr = zi * zi;
        zrsqr = zr * zr;

Celtic Burning Ship 4th Partial Real Mbar:
        zi = -4 * abs(zr) * zi * (zrsqr - zisqr) + JuliaI;
        zr = abs(zrsqr * zrsqr + zisqr * zisqr - 6 * zrsqr * zisqr) +JuliaR;
        zisqr = zi * zi;
        zrsqr = zr * zr;

Buffalo 4th:
        zi = abs(4 * zr * zi * (zrsqr - zisqr)) + JuliaI;
        zr = abs(zrsqr * zrsqr + zisqr * zisqr - 6 * zrsqr * zisqr) +JuliaR;
        zisqr = zi * zi;
        zrsqr = zr * zr;

Buffalo 4th Partial Imag:
        zi = abs(4 * zr * zi * (zrsqr - zisqr)) + JuliaI;
        zr = zrsqr * zrsqr + zisqr * zisqr - 6 * zrsqr * zisqr +JuliaR;
        zisqr = zi * zi;
        zrsqr = zr * zr;


Celtic (Buffalo 4th Partial Real):
        zi = 4 * zr * zi * (zrsqr - zisqr) + JuliaI;
        zr = abs(zrsqr * zrsqr + zisqr * zisqr - 6 * zrsqr * zisqr) +JuliaR;
        zisqr = zi * zi;
        zrsqr = zr * zr;

Celtic 4th Mbar:
        zi = -4 * zr * zi * (zrsqr - zisqr) + JuliaI;
        zr = abs(zrsqr * zrsqr + zisqr * zisqr - 6 * zrsqr * zisqr) +JuliaR;
        zisqr = zi * zi;
        zrsqr = zr * zr;


***Quasi ABS Variations (10)


False Quasi Perpendicular 4th:
        zi = -4 * zr * zi * abs(zrsqr - zisqr) + JuliaI;
        zr = zrsqr * zrsqr + zisqr * zisqr - 6 * zrsqr * zisqr +JuliaR;
        zisqr = zi * zi;
        zrsqr = zr * zr;

False Quasi Heart 4th:
        zi = 4 * zr * zi * abs(zrsqr - zisqr) + JuliaI;
        zr = zrsqr * zrsqr + zisqr * zisqr - 6 * zrsqr * zisqr +JuliaR;
        zisqr = zi * zi;
        zrsqr = zr * zr;

Celtic False Quasi Perpendicular 4th:
        zi = -4 * zr * zi * abs(zrsqr - zisqr) + JuliaI;
        zr = abs(zrsqr * zrsqr + zisqr * zisqr - 6 * zrsqr * zisqr) +JuliaR;
        zisqr = zi * zi;
        zrsqr = zr * zr;

Celtic False Quasi Heart 4th:
        zi = 4 * zr * zi * abs(zrsqr - zisqr) + JuliaI;
        zr = abs(zrsqr * zrsqr + zisqr * zisqr - 6 * zrsqr * zisqr) +JuliaR;
        zisqr = zi * zi;
        zrsqr = zr * zr;

Imag Quasi Perpendicular / Heart 4th:
        zi = 4 * zr * abs(zi) * abs(zrsqr - zisqr) + JuliaI;
        zr = zrsqr * zrsqr + zisqr * zisqr - 6 * zrsqr * zisqr +JuliaR;
        zisqr = zi * zi;
        zrsqr = zr * zr;

Real Quasi Perpendicular 4th:
        zi = -4 * abs(zr) * zi * abs(zrsqr - zisqr) + JuliaI;
        zr = zrsqr * zrsqr + zisqr * zisqr - 6 * zrsqr * zisqr +JuliaR;
        zisqr = zi * zi;
        zrsqr = zr * zr;

Real Quasi Heart 4th:
        zi = 4 * abs(zr) * zi * abs(zrsqr - zisqr) + JuliaI;
        zr = zrsqr * zrsqr + zisqr * zisqr - 6 * zrsqr * zisqr +JuliaR;
        zisqr = zi * zi;
        zrsqr = zr * zr;

Celtic Imag Quasi Perpendicular / Heart 4th:
        zi = 4 * zr * abs(zi) * abs(zrsqr - zisqr) + JuliaI;
        zr = abs(zrsqr * zrsqr + zisqr * zisqr - 6 * zrsqr * zisqr) +JuliaR;
        zisqr = zi * zi;
        zrsqr = zr * zr;

Celtic Real Quasi Perpendicular 4th:
        zi = -4 * abs(zr) * zi * abs(zrsqr - zisqr) + JuliaI;
        zr = abs(zrsqr * zrsqr + zisqr * zisqr - 6 * zrsqr * zisqr) +JuliaR;
        zisqr = zi * zi;
        zrsqr = zr * zr;

Celtic Real Quasi Heart 4th:
        zi = 4 * abs(zr) * zi * abs(zrsqr - zisqr) + JuliaI;
        zr = abs(zrsqr * zrsqr + zisqr * zisqr - 6 * zrsqr * zisqr) +JuliaR;
        zisqr = zi * zi;
        zrsqr = zr * zr;


Special thanks to Kalles Fraktaler and Command Line Cowboy for adding most of my 2nd and 3rd order fractals to their software plugins. Feel free to use any of the above formulas in any software program, image, or video render. Credit is appreciated but not required. Thanks for viewing...

See Also:

2nd Order ABS Formula:
stardust4ever.deviantart.com/a…

3rd Order ABS Formula:
stardust4ever.deviantart.com/a…

4th Order ABS Formula:
stardust4ever.deviantart.com/a…

5th Order ABS Formula:
stardust4ever.deviantart.com/a…

EDIT: April/08/2016 - Corrected some errors and added six fractals to complete all ABS() variations!