I wrote: << I don't know why fractals in 3-space would need to be based on something so very analogous to the Mandelbrot or Julia sets in the plane. There are plenty of other mappings one might experiment with, like the real polynomial mappings (x,y,z) -> (P(x,y,z), Q(x,y,z)). I don't think a great deal is known about these even if P and Q are only quadratic polynomials.
but this should have read: << I don't know why fractals in 3-space would need to be based on something so very analogous to the Mandelbrot or Julia sets in the plane. There are plenty of other mappings one might experiment with, like the real polynomial mappings (x,y,z) -> (P(x,y,z), Q(x,y,z), R(x,y,z)). I don't think a great deal is known about these even if P, Q, R are only quadratic polynomials.
--Dan Those who sleep faster get more rest.