Comments on: Connectedness.

By: Peter_D

Peter_D — Sat, 05 Mar 2011 15:42:08 +0000

Time that I had to spend to learn basics of algebra (even though I din’t have to) was definately not wasted, since I do understand now how this fractal is created. I just love this pure mathematical beauty. Thank You for giving the chance to admire this set in such a great quality.

Btw. Maybe I just haven’t found this on your website, but could you also draw Newton’s fractals?
especially for:
p(z) = z5 − 1

By: teamfresh

teamfresh — Wed, 02 Jun 2010 11:27:35 +0000

good idea. I will make an iteration movie and add it to the post soon

By: ethaniel

ethaniel — Wed, 02 Jun 2010 09:22:07 +0000

Nice explanation! Connectedness. I think an animated gif with one LONE iteration per frame may help show the exponentially increasing complexity without the previous iterations distracting.

Interesting how each fold of each iteration is a copy and yet unique… kinda like… everything

By: garett

garett — Tue, 01 Jun 2010 02:30:01 +0000

I don’t get this AT ALL! But I kinda like it. Next dog i get will be named mandelbrot, fer shur.

By: teamfresh

teamfresh — Mon, 08 Mar 2010 22:32:32 +0000

Thanks Tim, I’m glad you like this article. I try to explain fractals in a way that people who are not hardcore maths fans will find easy to read and understand – although I think that maybe you are not like that! I remember when I first came across the Mandelbrot set and though I had the pleasure of using a pc to create the image, it still took a full 20 mins to draw the whole set and I could only magnify it around 10 times before the computer choked and crashed – nether the less I would reboot and try again and again searching around the set and wondering at the beauty of infinity played out on the complex plane, oh how things have moved on! of course with the set being infinitely deep I will never be satisfied as no matter how powerful the computer in the end I always hit a wall in the computing power as I plunge ever deeper into the fractal – It is nice to be able to save these journeys though and I love to share them – on youtube – vimeo and where ever else I can. Indeed the chaotic nature of society can be seen in these patterns and I appreciate your interest.
as for your hexagonal head – check me out – I think nothing beats looking like a tic-tac!!!!

By: Tim

Tim — Mon, 08 Mar 2010 21:35:56 +0000

Now I’m REALLY impressed! How did you know I wear glasses and have a hexagonal head?

By: Tim

Tim — Mon, 08 Mar 2010 21:32:03 +0000

Terrific work. Can only suggest more YouTube posts to capture the imaginations of more people. I didn’t know about the connectedness, although it’s probably be derivable from just looking. BTW, I generated the ‘entire’ Mandelbrot Set on a Commodore 64 back in the eighties – wrote the program in C64-BASIC, ran it, and went out for the rest of the day. Came home and there it was on my screen, in monochrome. But I didn’t know how to save the image, nor could I have – I had no non-volatile storage at the time, so I had to turn the machine off and lose it all. But I did it. That is the only program I ever wrote that had non-textual output. Thanks to Douglas Hofstadter for the original interest. BTW2, my first 2 computer programs written on a IBM PC were also inspired by D.H. and Martin Gardener respectively. The first I don’t know how to describe anymore, the second was a John Conway Game of Life cellular automata that output 48×48 square grid and could have wrap turned on or off as well as having its rules altered. It used ASCII graphic chrs for output. I learned about the chaotic nature of society just by looking at the evolution of initial random patterns and imagining the squares were busy people.

By: teamfresh

teamfresh — Mon, 05 Oct 2009 15:59:40 +0000

Glad you like the content! I add posts and images every week.

By: Gabriele

Gabriele — Mon, 05 Oct 2009 15:56:21 +0000

Mesmerizing stuff on this blog. Fantastic colors…A bit of a puzzle… A ver, as the Spanish say which means that I shall see and will be educated about all this… Eventually…