#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.

[vedalkensamurai]

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

[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.

[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]

z_(n+1) = e^(z_n) + e^(z_n^(i^(4t))) - 2 + c for t from 0 to 1

[vedalkensamurai]

z_(n+1) = i^(4t) * sin(z_n) + c if n is even

z_(n+1) = i^(-4t) * sinh(z_n) + c if n is odd

t grows from 0 to 1.

[vedalkensamurai]

z_(n+1) = e^(1 + a₁(z_n) + a₂(z_n)² + a₃(z_n)³ + a₄(z_n)⁴) + c

All the as start at 0, then a₁ begins to grow. When it reaches 1, it stops, and a₂ begins to grow, and on up the chain until all four as are 1.