Fractal: an object whose Hausdorff-Besicovitch dimension is greater than its topological dimension.
Kudos to you if you understand and can define the definition in English...
* Is there anyone here that creates these? * Are there other computer programs that anyone can recommend besides the one I mention below? * Has anyone used FLAM3? * Anyone just like Fractals and have a few favorites they'd be willing to share?
The following are Fractal Art Images, created by Sven Geier using a free download of a program called FLAM3 (which can be accessed from the same site). Sven has made these, and a vast array of other examples, available for common use (see the site for details) at the following site: The Fractal Bargain Bin - Wallpapers / Eye Candy / Pretty Stuff.
Hmm, no mathematician, but I was lucky to see a talk by BenoĆ®t Mandelbrot once, which inspired me to read his book 'The fractal geometry of nature'. As far as I got it, the topological dimension is a natural number <em>n</em> (0 for point, 1 for line, 2 for plane etc...) Now, if you create fractal structures consisting of n-dimensional elements (such as the recursive Sierpinski triangle, you know, the triangle divided into more triangles into infinity), that structure has a real-valued dimension (1.58 f.ex.), also called fractal dimension.
I'm having a time out until I can learn some manners.
<a target="_blank" href="http://deputy-dog.com/2007/11/01/11-phenomenal-images-of-earth/">These</a> were made without software but are kind of interesting...
The eastern coast of Greenland, looking very fractal-like:
lex: Alright...I actually understood that...and that scares me a little as I won't even pretend to be a math oriented person.
I think that talk by Mandelbrot would have been interesting, though...did he provide visuals?
Obliterati: WOW!!! They're all wonderful, but I absolutely LOVE the first one in the series you've posted above.
...and now I've had a look at the ones from the link you've provided and I'm just blown away. In that series, I really like the last one from the desert.
There are some fractals you can grow in your garden: Romanesco
I remember the talk by Mandelbrot only vaguely as it was quite a long time ago, but he definitively gave visuals (among others the Romanesco), as it was targeted at a general audience in a modern art museum, the ZKM in Karlsruhe, Germany.
wow. very nice post, obliterati. off to find out more now!
Anyone who remembers the Fight Club intro sequence with the brains, that was done using a L-System, still one of my favorite 3D sequences. Currently, houdini has the best implementation of fractals and recursive and procedural workflow in my opinion... SideFx they have a free version you can play with. A bit weird to learn, but great fun.
I'll always remember finding Lapre's 3D L-Parser when I was at college, and it kept me awake for nights. For anyone interested there are a number of l parser implemented in different apps, there is one in inkscape.
Dag nabbit! I had the video all loaded and everything and was going to watch it as soon as I could get to a point where I could turn up the volume...but I got distracted with downloading fractal programs and navigated away from here with the wrong page...hope it comes back up.
@Mark Seifert I just downloaded contextfree...Thank you for posting the link. I look forward to trying it out. I've only downloaded a pdf explaining FLAM3 so far...lol...I think contextfree looks a bit easier.
@aike Thank you; Houdini looks like an awesome program! Got the "Apprentice" version and I'm really looking forward to seeing what it can do!