Title: Circlebox trip Post by: bib on July 12, 2010, 08:58:10 PM A zoom into an Amazing box/octahedron hybrid
http://www.youtube.com/watch?v=bvrO4Wu94Do (http://www.fractalforums.com/gallery/2/492_09_07_10_7_02_32.jpeg) Title: Re: Circlebox trip Post by: miner49er on July 13, 2010, 01:51:10 PM Brilliant.
Would I be correct in saying that the Mandelbox provides a greater level of varience in detail to the Mandelbulb. I guess the two different objects are only related by the fact that they are both 'escape-time' fractals? I love it though and cannot get enough of these movies that you guys keep producing! Title: Re: Circlebox trip Post by: bib on July 13, 2010, 02:20:28 PM Thanks :)
The Mandelbox itself is quite varied (equivalent to Mandelbulb but more geometric patterns). What is nice with the Mandelbox is that it can combine very well with other geometric transforms to create incredibly varied hybrids (see all my videos on Youtube). The Mandelbulb can also be used to do hybrids, but combining bulbs and geometric shapes often leads to too chaotic shapes. Many "normal" people don't like fractals because of the too often seen Mandelbrot/julia set traditional shapes (spirals, flowers, etc...), so IMO the new wave of boxes and their 3D geometric patterns opens up new possibilities to address a much wider audience. Title: Re: Circlebox trip Post by: hobold on July 13, 2010, 05:46:59 PM I think the real reason why the Mandelbox has better variety of shapes is because it is based on conformal mappings ... in other words, it is guaranteed not to have (the equivalent of) whipped cream anywhere at all. The Mandelbulb in contrast is affected by whipped cream almost everywhere, in the sense that the stretchy mappings flatten most of it (especially visible in the ^2 version). We just are not aware of the whipped cream as much, because we direct our attention to the few remaining richer shapes.
In that sense, the Mandelbox is indeed a more faithful analog of the classical 2D Mandelbrot set. Plus, it's full of seemingly straight and circular features, which is rather refreshing for a fractal. Instead of an organic appearance, the Mandelbox has more of a technological or architectural feel. Title: Re: Circlebox trip Post by: miner49er on July 15, 2010, 02:29:02 PM Thanks for the replies guys :-)
I am very grateful to you for producing the pictures as I find them completely awe-inspiring (nearly said awesome there!) I just wish I had more time to explore these objects myself... Title: Re: Circlebox trip Post by: crotafang on July 21, 2010, 12:13:10 AM I applaud thee. I liked how you changed the colors and how you started by zooming out. :D :D |