#multibrot

z_(n+1) = z_n^(6.5 + 9* |t - 0.5|) + i^(-4t) * c

“The quaternion mandelbrot set isn't very interesting to look at, since it's just the surface of revolution of the set as it exists in the complex plane into hypercomplex (quaternion) space. Having said that, this animation shows the evolving quaternion multibrot from power -6 to 6, which are all rotational symmetric sets in the real axis.“

t oscillates between 0 and 1.

Lemniscate II

3-brot with 72 orbit traps, traveling along randomly-selected interpolated 3-brot orbits. Non-escaping orbits are excluded.

z_(n+1) = 0.5 (1 + cos(t)) z_n⁴ - 0.5 (1 - cos(t)) (e^z_n² + e^z_n^-2 - 2) + c

9-brot with 9 point traps