Risto A. Paju
Julia sets of z^2 + c are the prototypical fractals. Their
familiarity makes them the perfect examples for demonstrating new
visual techniques, which in turn reveal new aspects of the sets
themselves. This short film is a sequel to my Bridges debut of 2016
and continues the quest for new Julia set variants. After a
retrospective beginning, the journey proceeds into newer extensions
of my IFS overlay graphing method, notably 3D functions. Between the
two worlds, an educational interlude with a comic relief breaks the
cadence. In the latter half of the film, two major 3D forms are
given special attention. The first is a joining of regular 2D Julias
into a stringy crossing, where the “c” parameter varies smoothly
along the third axis. (A familiar Julia form can be seen at the
beginning of that scene, as the shape starts to expand from a thin
slice.) The second is a series of “Julia bulbs”, the Julia sets of a
quadratic Mandelbulb.