If you're like me, then you hit 't' at the spash screen of FRACTINT instead of believing in default fractals or complaining about maps that disappear whenever you switch fractal types. It's worth noting that it's FRACTINT that defines negative periodicity, and it means "show your work". A picture is worth a hundred lies, so I'll mention that before I start: Methods { ; A look at the internals of tesseral, border ; tracing, and diffusion at the inversion of where x=1/3. reset=2003 type=mandel passes=t center-mag=-0.533722/6.10623e-016/0.9699869/1.5686/-90/-1.233735336114\ 70521e-014 params=0/0 float=y maxiter=255 fillcolor=2 inside=255 invert=0.47/-0.33333333333333333/0 periodicity=-2 colors=0zzzzz00zz0zz0Wz00zV0zz0<3>0z00zV0zz<3>00zV0zz0z<3>z00<3>ze0zo0\ zz0Wz00z0<3>0ze0zo0zz<3>00zV0zz0z<3>z00<3>ze0zo0zz0<3>Lz0Bz00z00zV0zz<\ 3>0Lz0Bz00z<3>z0zz0Wz00<3>ze0zo0zz0<3>0z0<3>0ze0zo0zz<3>0Wz0Oz0Gz08z00\ z<3>z0zz0Wz00<3>zz0Wz00z0<3>0zz<7>0Rz0Nz0Iz<3>00z<3>z0z<3>z0Lz0Bz00zV0\ zz0<3>az0Wz0Qz0<3>0z00zV0zz<3>0Lz0Bz00z<3>e0zo0zz0z<3>z00<3>ze0zo0zz0<\ 3>Lz0Bz00z00zV0zz<3>0az0Wz0Qz<3>00zV0zz0z<3>z00zV0zz0<5>Wz0Rz0Lz0<3>0z\ 0<5>0zV0z_0ze<3>0zz<3>00zV0zz0z<3>z00<3>ze0zo0zz0Wz00z0<3>0zP0zV0z`<3>\ 0zz<3>000 } Bogus, my cat, was last seen evading American Foreign Policy on a rocket destined to annoy Marvin The Martian. I had a joke about "advanced connect the dots" in high school that I thot was funny, so little did I know that the mathematic art form could safely be called "Advanced Paint By Number" to piss off the blondes who thot they knew all about that. In the above "methods", you would see three critical rejions; White On Blue: First Escapees. Black On Blue: Rejion of unlikelyhoods. Yellow On Blue: Rejion of dispute. [Negativ periodicity is required to make border tracing work in this example, so if you zoom or pan this fractal to where border tracing yields what could be mistaken for a dubl fawlt, then try a more pessimistic number.] The rejion of dispute is the only part that rendering this fractal with passes=diffusion will highlight. Border tracing will highlight all of the mandeloids (physically on the outside, while mathematically on the inside of an inversion), while tesseral makes for a clear-cut reminder that this is art in the midst of analytic minds -- where geers and artsies work together with bounded chaos. This rejion is yellow on blue. If a bug is here, then it looks kinda cool, so maybe THIS should be the default parameters, no matter what you think of periodicity checking. Perhaps periodicity should be moved to the X-screen, while one of the doo-dads like biomorph or decomp (that don't seem to apply to orbital fractals, either) can move to Y. Synchronous Orbits? That's so close to the bleeding edge that it doesn't work with inversions. Now, as an excercise for the reader, which means I'm too lazy to answer the question myself: Why does border tracing require colour number zero?