Antarctic Ships, Fractal and Real

Posted by Cleve Moler,

David Wilson, from the Auckland University of Technology in New Zealand, has alerted me to this remarkable coincidence. Here is the "Burning Ship" from my post about fractals four weeks ago.... read more >>

Greg Searle, Fractal Art and Design

Posted by Cleve Moler,

If you follow this blog regularly, you know that I love fractals. I recently spent a pleasant afternoon in Nashua, New Hampshire, where my daughter Teresa introduced me to Gregory Searle, a fractal artist and computer geek. Here is his logo.... read more >>

Season’s Greetings Fractal6

Posted by Cleve Moler,

I don't recall where I found this seasonal fractal. And I can't explain how it works. So please submit a comment if you can shed any light on either of these questions.... read more >>

Fractal Global Behavior of Newton’s Method

Posted by Cleve Moler,

When the starting point of Newton's method is not close to a zero of the function, the global behavior can appear to be unpredictable. Contour plots of iteration counts to convergence from a region of starting points in the complex plane generate thought-provoking fractal images. Our examples employ the subject of two recent posts, the historic cubic $x^3-2x-5$. ... read more >>

Season’s Greetings, 20142

Posted by Cleve Moler,

Season's Greetings, 2014 help greetings % greetings Seasonal holiday fractal. % greetings(phi) generates a seasonal holiday fractal that depends % upon the parameter phi. The default value of phi is the golden ratio. % What happens for other values of phi? Try both simple... read more >>