Spirals in the M-set come in two flavors, either the center is a Misieurewicz point (in which case they are infinitely deep) or they eventually resolve to real detail with a minibrot in the middle. You can tell when you're on your way to the latter because you'll start to see the classic period-doubling effect, where detail forms in rings around the center point and each nested ring has twice as many copies of the detail around it. The trick is recognizing which is which! In the East "elephant" valley, the spirals that make the elephant snouts are M-points, but if you look at the detail that makes up the spiral arm, you'll see spirals linked by clusters. That cluster is a minibrot, all those clusters have minibrots, all the way down the spiral. However coming off those minibrots are two extra spirals that don't link to anything else; the centers of those spirals are M-points just like the main spiral. After a while you can learn to identify by "feel" which spirals are M-points and which contain minibrots. Then you can safely zoom even into extended precision, confident eventually you'll reach your minibrot. Damien M. Jones dmj@fractalus.com http://www.fractalus.com/gallery/ http://www.damienmjones.com/