Image of the Week #75

This is a 50-frame animation of an increasing iteration number for a scalloped convergence Mandelbrot set.



Image of the Week #73

This one is a scalloped convergence Mandelbrot set on a fairly deep zoom.  Later I may move into the central sun and see what’s there.  The black tentacles at the edge are a bit Lovecraftian?


Image of the week #68

This is another fourth-power Mandelbrot set — at the looks-like-chocolate level of zoom.  It is rich in oddly-polygonal looking basins of attraction.  Star lake on Chocolate island.IOTWb.png

Fractal Lenses


Occupy Math has already taken a shot at explaining what fractals are. He has tried to supply engaging holiday fractals. On of the least popular posts is on the incredible complexity of the Mandelbrot Set and there is a post on making family trees of fractals (and other things). What’s left? This week Occupy Math is going to turn up the weird to eleven and use fractal algorithms as lenses — a different type of lens from the one shown at the top of the post. The only thing you really need to know about fractals to get a sense of what is going on is that a fractal is based on an algorithm that moves a point around in a complex way until it is captured. The details of the algorithm and the conditions for “capture” give you the shape and then you also need a coloring algorithm. Today’s post is all about a really odd way to color fractals.

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Image of the Week #64

This week we have a generalized Julia set with the interior of the set colored using a shade of yellow and the cosine coloring algorithm.  This yields a pleasant, metallic appearance.IOTW64

Image of the Week #63

This is a context shot on a meandering fractal river in the Mandelbrot set.  It uses a new type of convergence called wedge convergences that deems a point to have diverged when they move into cones with a vertex at one of (1,1) (1,-1) (-1,1) and (-1,-1).IOTW