A few months ago, I had never heard of Karl Menger or the cube-like fractal that he invented. Now I have this long blog post about the sponge, and an extension that I am calling its "associate".... 続きを読む >>

The complement of an evolving Menger sponge is all of the material that has been removed so far.... 続きを読む >>

Season's Greetings 2021 __________________________________________________________Marc Lätzel (2021). XMas Tree (https://www.mathworks.com/matlabcentral/fileexchange/9337-xmas-tree),MATLAB... 続きを読む >>

The Menger sponge is a popular fractal that generalizes Cantor sets and Sierpinski triangles. Its fractal dimension is between two and three.... 続きを読む >>

Mandelbrot Brings Season's GreetingsMandelbrot sports a new red, green and gold colormap to celebrate the holidays. old_mandelbrot holiday_mandelbrot Available in Version 4.10 of Cleve's... 続きを読む >>

Antarctic Ships, Fractal and RealDavid 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... 続きを読む >>

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.... 続きを読む >>

Let me tell you about a beautiful, fractal curve, the Dragon Curve. Download my new dragon program from the File Exchange and follow along.... 続きを読む >>

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.... 続きを読む >>

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 $x^3-2x-5$. ... 続きを読む >>