Infinite tetration fractal pictures - Printable Version +- Tetration Forum (https://math.eretrandre.org/tetrationforum) +-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1) +--- Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3) +--- Thread: Infinite tetration fractal pictures (/showthread.php?tid=144) Pages: 1 2 Infinite tetration fractal pictures - bo198214 - 04/12/2008 Hello, I was a bit under the impression (probably by looking at the depictions at Daniel's site) that tetration fractals are somewhat ugly. However as I now discovered and as I want to share with you thats absolutely not the case. The following fractals are all generated with Fractal Explorer, the real/x axis is top-down, while the imaginary/y axis is left-right (picture symmetry just look better this way). For the iterations we start with the value of the pixel as a complex number $z_0$ and then compute iteratively $z=z_0^z$. If $|z|$ gets over a certain threshold, then the number of iterations necessary for doing so is coded with colors. Black means it never gets over the threshold (at least not below the maximum of iterations performed). Now have fun! I start with the an overview picture: [attachment=294] The coordinate origine is roughly amidst the claws of the small lobster hanging down. And $e^{1/e}$ is roughly at the top of the middle stalagmite. If someone wants to experiment for him/herself the fractalexplorer source file is attached. RE: fractals - bo198214 - 04/12/2008 [attachment=295] [attachment=296] the following is a small dot magnified that resides even above the previously depicted structures but is not visible on the overall picture. [attachment=297] RE: fractals - bo198214 - 04/12/2008 [attachment=298] [attachment=299] [attachment=300] RE: fractals - bo198214 - 04/12/2008 [attachment=301] [attachment=302] [attachment=303] RE: fractals - bo198214 - 04/12/2008 [attachment=304] This is the small lobster hanging down: [attachment=305] [attachment=306] [attachment=307] RE: Infinite tetration fractal pictures - andydude - 04/13/2008 Nice! I like these fractals! My only question is the coloring method used? because this seems to be the only difference to me, or if there is a procedural difference as well. For example: by period, by escape, etc... Anyways, I also wanted to understand the context of the larger overview image, so I super-imposed it with the one from Geisler's site: [attachment=309] although I probably should have kept it vertically symmetric since both Juan de Mairena and Ioannis Galidakis seem to think this is the way it should be viewed as well... Andrew Robbins RE: Infinite tetration fractal pictures - bo198214 - 04/13/2008 andydude Wrote:My only question is the coloring method used? Oh its individually adapted for artistic purpose In fractal explorer you define a color gradient for the range of iterations, that is a curve (with x axis being the range of iterations) for each of the red, green and blue component. Quote: because this seems to be the only difference to me, or if there is a procedural difference as well. For example: by period, by escape, etc... As I described these pictures are just by escape. So periods and convergence areas are equally black. Quote:Anyways, I also wanted to understand the context of the larger overview image, so I super-imposed it with the one from Geisler's site: and became that context (whatever you mean by this) now clear? tetration fractal spirals - bo198214 - 04/15/2008 I created some more awesome pictures with focus on spirals in the fractal. I changed the software from "fractal explorer" to chaos pro which is somehow more prefessional when needed for fluidly navigating a fractal and it is especially faster. As it is perhaps somewhat cumbersome (for the viewer) to put the photos directly in the thread I decided to make a small gallery and just put a snapshot of the thumbnails here (to navigate them just go to my gallery): RE: Infinite tetration fractal pictures - Gottfried - 04/15/2008 Hi - really nice! To add even more beauty (and also make it more usable...:cool I converted some into "plakette"-type (german; english: "plate"?) to put it, for instance, into silver and wear it as necklace... [attachment=311] and [attachment=312] or smaller [attachment=313] Gottfried RE: Infinite tetration fractal pictures - bo198214 - 04/15/2008 Gottfried Wrote:I converted some into "plakette"-type (german; english: "plate"?) to put it, for instance, into silver and wear it as necklace...yes but then you really have to use the necklace!