#escape time algorithm

[vedalkensamurai]

Descendelbrot

z_(n+1) = (z_n)^(2 - sin(arg(c)/2 - t)^20) + c

In most of the image, the power is (very close to) 2, but in a narrow, rotating pie-slice it decreases smoothly to 1.

[dl-art-abstract]

Abstract vibrant and colorful fractal 10

[vedalkensamurai]

z_(n+1) = i^(4t) * sin(z_n) + c if n ≡ 0 (mod 4)

z_(n+1) = i^(4t + 2) * sin(z_n) + c if n ≡ 1 (mod 4)

z_(n+1) = i^(4t + 2) * sinh(z_n) + c if n ≡ 2 (mod 4)

z_(n+1) = i^(4t) * sinh(z_n) + c if n ≡ 3 (mod 4)

[vedalkensamurai]

z_(n+1) = e^(iz_n² + z_n) + i^(4t) e^(iz_n² + i^(4t) z_n) - (1 + i^(4t)) + c

[vedalkensamurai]

Mandelbrot set with escape time coloring, but the red, green, and blue channels use different iteration maximums, ranging between 64 and 6400.

[vedalkensamurai]

z_(n+1) = z_n^(6 - t) * e^(z_n^t + z_n^-t) + (-1)^n * c - 1

t grows from 1 to 2. Rotated 90° clockwise.

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[vedalkensamurai]

Smoothly transitioning from the Mandelbrot fractal to the Burning Ship fractal by adjusting just how absolute those values are.

[vedalkensamurai]

Maybe you've noticed that the graph of y = e^-x + e^x looks rather similar to a parabola. Does that mean that using that formula as the basis of an escape-time algorithm will result in a fractal that looks similar to the Mandelbrot set?

Yes. Yes it does.