This post contains an activity you can do with a calculator, a bit of a magic trick. The post is also about a very special number called the golden ratio. The golden ratio is not as famous as pi or e, but it keeps showing up again and again in multiple contexts. The spiral above is made by choosing quarter-circles that cover two earlier quarter circles, along their sides. After going through the activity, Occupy Math will reveal how this spiral involved the golden ratio.
A Newton-Julia flower with large borders, to achieve a cartoon like appearanace.
This week we look at a mixed type Julia set with a cubic iterator followed by a quadratic iterator. Note the interesting central structure.
This week we take a Newton’s method fractal, with fifteen roots, and show how it forms in an animation. Sorry for the small size — animation uses multiple pictures so it makes big images.
A newton monster fractal with internal organs!
This week, a Newton’s method fractal that shows what can happen when a couple of roots are close together. Spider temple?
One of Occupy Math’s research areas is figuring out how to get computers to produce game content more-or-less automatically. This post announces a book that summarizes many of Occupy Math’s findings. You can buy a copy from my publisher Morgan and Claypool, but if you are part of a university or other institution that subscribes to the Morgan and Claypool synthesis series then an e-book with unlimited use for students and faculty will show up in your library presently. Profits go to Occupy Math’s consulting company, which funds students and research!
This is a deep zoom into the cubic mandelbrot using leaf convergence. It has an odd, finished character.
This week we have an activity that Occupy Math has used for math activity nights at schools. There is often a shortage of activities for younger children at a school math night and today’s post hopes to help with that. An earlier post on kid’s math books includes the idea of a reading table that gets parents and young children involved. The activity Construction by Instruction appears in the post on cooperative games. This week is the activity Tiling the Wall
This is a Julia set with three complex parameters located with an evolutionary algorithm. It’s part of an on-going automatic fractal location program.