The software I use
(FractInt)
has this to say about magnetic fractals:
These fractals use formulae derived from the study of hierarchical lattices, in the context of magnetic renormalisation transformations. This kinda stuff is useful in an area of theoretical physics that deals with magnetic phase-transitions (predicting at which temperatures a given substance will be magnetic, or non-magnetic). In an attempt to clarify the results obtained for real temperatures (the kind that you and I can feel), the study moved into the realm of Complex Numbers, aiming to spot Real phase-transitions by finding the intersections of lines representing Complex phase-transitions with the Real Axis. The first people to try this were two physicists called Yang and Lee, who found the situation a bit more complex than first expected, as the phase boundaries for Complex temperatures are (surprise!) fractals.One gets the feeling that perhaps FractInt's authors don't understand the science behind it any more than I do, but don't have any objections to using the formulae to make fractals. And here those formulae are: |
Magnet 1 |
Magnet 2 |
c and z are used just like c and z for regular Julia and Mandelbrot fractals - c is fixed for Julias, and varies for Mandelbrots. z represents each point. These formulae are considerably more complex than the standard Mandelbrot & Julia formula, and it takes a lot longer to make pictures of these fractal types. |
Magnet 1 |
Magnet 2 |