This week we look back at the great-tree region of the fourth order Mandelbrot set under quadrant convergence.

# Pretty Pictures

# Image of the week #81

This images is a second-fifth order hybrid Mandelbrot set. The short version? It’s never done this before.

# Image of the Week #80

This is a view from the cubic Mandelbrot set using quadrant convergence. Its another example of an abrupt change in the colors creating an island.

# Image of the Week #79

This week, the Newtons method fractal of a 27-root polynomial with complex coefficients. The input is random but the algorithm is not!

# More math evolution is good at!

In Evolution Can Do Math That People Can’t, Occupy Math showed how to use digital evolution to create a self-limiting type of cellular automaton (apoptotic cellular automata) that are pretty to look at. These cellular automata also have their own mathematical version of “genetic material” that could be used in breeding experiments — one of which appears in the post. This work is a combination of mathematics with theoretical biology. In this post, Occupy Math will look at *Cavern Automata *which are used for gamining maps. A picture made with one of these automata appears at the top of the post. The rule that specifies how to make pictures like the one above was evolved, just like the rules for the pretty pictures in the earlier post.

# Image of the Week #78

This week the image is drawn from the 2-3-2 Mandelbrot set, a fractal generated by applying the squared and cubed Mandelbrot iterators in the pattern 2-3-2-2-3-2-2-3-2-etc. Some parts of this set are pretty irregular, others look like slightly different versions of the ordinary squared set. This image is a Minibrot with the classical squared shape but a moderately odd surrounding texture.

# Images of the Week #77

In this post Occupy Math is trotting out some classic Newton’s method fractals each of which evokes some animal. There are four so some scrolling may be needed.

# Image of the Week #76

This image is taken from the cubic Mandelbrot set, using *diamond convergence*. It is a fairly deep zoom.

# 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 #74

Another scalloped Mandelbrot set — this time with a more vigorous set of collors!