Title: an interesting new type (a few days old actually) Post by: M Benesi on October 25, 2010, 03:59:49 AM I posted a few images over in the images forum when I discovered the formula. For z^2, it has a central spin hole where the main cardioid is in the 2d Mandelbrot: (http://lh6.ggpht.com/_gbC_B2NkUEo/TMTPmSjotbI/AAAAAAAAAxY/yu92pn6tuVg/straight%20on%20demo%20of%20main%20swirl.jpg) although it doesn't include the 2d Mandelbrot cross section, as it's more closely related to a burning ship fractal. It (the z^2) has little mini-swirls all throughout the body of the fractal, and some crystalline sections like: (http://lh3.ggpht.com/_gbC_B2NkUEo/TMEpwwg2s4I/AAAAAAAAAwE/dHT-XE4eh2w/zoom%206%20iterated%20more%20got%20wierd.jpg) And then there are the sections in which it is all twisted around itself: (http://lh6.ggpht.com/_gbC_B2NkUEo/TMTPmftoUyI/AAAAAAAAAxg/f2EZwXu4dSc/back%20more%20iterated.jpg) another zoom into the twistyness of the z^2: (http://lh4.ggpht.com/_gbC_B2NkUEo/TMTU9HKrfEI/AAAAAAAAAxs/XEizRs0qXSA/s400/back%20corner%20zoom%20big.jpg) That is just the z^2. The z^3 has interesting properties of its own, as does the z^4 (although I'd think that the properties of the z^3 and 4 are repeated through all the higher n(s), just different basic patterns). z^3 has these neat interconnected X things (well, they are more like an X and a + sign melded together): (http://lh5.ggpht.com/_gbC_B2NkUEo/TMTck_n1KhI/AAAAAAAAAyI/lEXxUWFQyLc/zoom%20zoom%20zoom%20zomma%20zoom%20zoom.jpg) And z^4.. well it has cool buildings, moats, and just some generally complicated patterns: First zoom into buildings: (http://lh3.ggpht.com/_gbC_B2NkUEo/TMTfcaUxfWI/AAAAAAAAAyc/9I5pOJCmOrc/the%20buildings.jpg) going towards 'em: (http://lh3.ggpht.com/_gbC_B2NkUEo/TMTfcOwm1_I/AAAAAAAAAyY/vtMwx_89xGc/fly%20into%20the%20building.jpg) iterated once: (http://lh4.ggpht.com/_gbC_B2NkUEo/TMTfcba2tTI/AAAAAAAAAyg/jonGrGNl1A4/zoom%20zoom%20zoom%20into%20the%20buildings.jpg) between the buildings (moat area between complexes of buildings), deep zoomed (well, 2 more iterations from above.. not tooo deep): (http://lh6.ggpht.com/_gbC_B2NkUEo/TMTfb7tqBJI/AAAAAAAAAyU/2w6kcVcoxxQ/in%20the%20moat.jpg) So there is lots of need stuff... anyways. |