Mandelbrot and Julia Sets

 Mandelbrot and Julia sets related to asymptotic behavior of iterated function in the complex plane. These 3D printed objects represent Mandelbrot and Julia sets not just of the standard quadratic function but also for other functions as well (some people refer to these generalized cases by other names such as multibrot sets). 

A stack of multiple Julia sets for z^2 + c along a fixed line of c values in the complex plane. 

Another view of the previous object above

Mandelbrot set for z^(3.5)+c

Mandelbrot set for (Sin(z^2)/Exp(z))-(c/2)

Left: Mandelbrot set for z^(15)+c - this set has 14 bulbs.
Right: Mandelbrot set for z^8+c, resulting in 7 bulbs. 

Filled Julia set for f(z) = z⁷ + c, where c= -0.8+-0.2i

Filled Julia set for z^2+z+(-1+.2i) - presumably the spikeyness is due to this being outside the Mandelbrot set, meaning that the Julia set is not connected.

Additional view of above object