Title: How distorted can a minibrot be? Post by: MateFizyChem on November 09, 2016, 10:02:46 PM Today I found this distorted minibrot. :evil1: Can it get more distorted like this?
Title: Re: How distorted can a minibrot be? Post by: MateFizyChem on November 09, 2016, 10:04:03 PM Oops, I thought that I was in the Mandelbrot subforum.
Title: Re: How distorted can a minibrot be? Post by: Sockratease on November 09, 2016, 11:18:40 PM Oops, I thought that I was in the Mandelbrot subforum. :gum: It is now! Title: Re: How distorted can a minibrot be? Post by: Chillheimer on November 10, 2016, 09:54:47 AM AFAIK you only find distorted minibrots in the seahorse-valleys/spiral-valleys. the closer you get to the attach-point of the bulb, the more distorted the minibrot will be. But distortion maxes out at a certain angle and the difference gets smaller and smaller if you go deeper into the valley.
Pretty sure someone here knows that angle and why that is - claude? Title: Re: How distorted can a minibrot be? Post by: DarkBeam on November 10, 2016, 12:00:44 PM I think there is no limit :D
Title: Re: How distorted can a minibrot be? Post by: hobold on November 10, 2016, 02:17:20 PM I have been trying to find the "most distorted" minibrot before, but my search was unsystematic. Can anyone provide some guidance on how to find "very" distorted minibrots?
To measure and compare distortedness, I suggest looking at the relative position where the largest disk (i.e. the one with the main antenna) is attached to the minibrot's cardioid. The further away from the normal position (opposite to the cardioid's cusp) the main disk is, the more distorted I'd call the minibrot. I have never seen a minibrot where the main disk was rotated more than sixty-something degrees away from its ordinary position. Has anybody ever found a minibrot with an asymmetry of 90 degrees or even more? (Edit: the example image by the thread starter would be rated thirtysomething degrees, I guess.) Title: Re: How distorted can a minibrot be? Post by: claude on November 10, 2016, 06:59:59 PM AFAIK you only find distorted minibrots in the seahorse-valleys/spiral-valleys. the closer you get to the attach-point of the bulb, the more distorted the minibrot will be. But distortion maxes out at a certain angle and the difference gets smaller and smaller if you go deeper into the valley. Yes I found that too. Quote Pretty sure someone here knows that angle and why that is - claude? not me! I did find some research from 1994, but it's just quantifying the distortions, not searching for the most distorted: Warped midgets in the Mandelbrot set A.G.Davis Philip, Michael Frame, Adam Robucci Quote Warped midgets in the Mandelbrot set have been measured, using an algorithm that allows the positions of the head, and cardioid atoms (north and south) of any midget to be found, once one has placed the cursor on the computer terminal somewhere inside any midget. We describe two distortions of midgets: linear distortions and angular distortions. When the north and south angles are plotted in the north/south angle plane, families of points are formed. The angle and distance measures of warped midgets from the Sea Horse Valley of the Mandelbrot set and from other sea horse valleys of midgets, whether on the Spike or on tendrils above atoms, all fall closely together in one part of the north/south plane. Measures of warped midgets from tendrils above the major atoms on the surface of the Cardioid fall closely together in another part of the north/south plane. This different way of looking at the Mandelbrot set offers an interesting way of studying the distortions of midgets. http://www.sciencedirect.com/science/article/pii/009784939490099XTitle: Re: How distorted can a minibrot be? Post by: MateFizyChem on November 10, 2016, 09:26:03 PM I found this cute apple. Small difference, big disappointement. :sad1:
Real number position: 0,25000102515011806826817597033225524583655 Imaginary number position: 0,0000000016387052819136931666219461 Zoom: 6,871947673*(10^10) How about a competition for finding the biggest distortion(Wait, has the distortion even got a name?)? Title: Re: How distorted can a minibrot be? Post by: xenodreambuie on November 10, 2016, 10:05:48 PM The largest minibrot in each elephant or similar shape in most valleys on the right side has similar distortion.
Looking at other formulas (without using any Abs modes or trig functions to really add distortion), it can get worse. Here are some in (z^5+z+1)/(2z^2-1)+c; the two smaller minis are mutants compared to the large one. Title: Re: How distorted can a minibrot be? Post by: MateFizyChem on November 10, 2016, 10:42:24 PM The largest minibrot in each elephant or similar shape in most valleys on the right side has similar distortion. (I am hoping that I did not fail at quoting the image.)Looking at other formulas (without using any Abs modes or trig functions to really add distortion), it can get worse. Here are some in (z^5+z+1)/(2z^2-1)+c; the two smaller minis are mutants compared to the large one. (http://www.fractalforums.com/index.php?action=dlattach;topic=24799.0;attach=13570;image) Larvae! Kill them, before these parasites will eat us inside out!!! :canadian: But it seriously is as amazing to me, as the mandelbrot set is to a new person in fractals. :happy: Title: Re: How distorted can a minibrot be? Post by: claude on November 11, 2016, 07:49:05 PM some fun with conformal transformations :D
(https://mathr.co.uk/mandelbrot/2016-11-11_conformal_warping.gif) Title: Re: How distorted can a minibrot be? Post by: MateFizyChem on November 11, 2016, 08:40:30 PM Well, I deduced that, the closer a minibrot to zero, the smaller is the difference between a neighbouring minibrot and the found minibrot when it comes to the distortion, so there probably is a limit to the distortion.(Have I made myself clear?)
I am suggesting to measure the distortion in degrees(or radians), because no half is smaller(I thought so :embarrass:), the parts of the minibrot are simply rotated. The 2nd picture is distorted by around 35 degrees(WARNING: I DID NOT MEASURE IT EXACTLY; THE MEASUREMENT MIGHT BE WRONG). Title: Re: How distorted can a minibrot be? Post by: Sockratease on November 11, 2016, 10:37:22 PM some fun with conformal transformations :D Reminds me of my new avatar image O0 (http://nocache-nocookies.digitalgott.com/gallery/0/162_14_05_08_1_06_35.gif) Title: Re: How distorted can a minibrot be? Post by: MateFizyChem on November 12, 2016, 05:41:16 PM So, has anyone got a hypothesis or a theory?
Quote How distorted can a minibrot be? Title: Re: How distorted can a minibrot be? Post by: claude on November 12, 2016, 06:38:59 PM Here's some visual evidence showing the convergence to a limit of distortion in elephant valley, with the period doubling each frame:
(https://mathr.co.uk/mandelbrot/2016-11-12_warped_midgets.gif) locations: Code: 4 -1.565201668337550811e-01 + 1.032247108922831780e+00 i @ 1.697e-02 Title: Re: How distorted can a minibrot be? Post by: MateFizyChem on November 12, 2016, 07:32:59 PM Here's some visual evidence showing the convergence to a limit of distortion in elephant valley, with the period doubling each frame: (https://mathr.co.uk/mandelbrot/2016-11-12_warped_midgets.gif) locations: Code: 4 -1.565201668337550811e-01 + 1.032247108922831780e+00 i @ 1.697e-02 So I am assuming that the 1st hypothesis is (inaccurately measured) 30 degrees. Title: Re: How distorted can a minibrot be? Post by: hobold on November 13, 2016, 08:10:35 AM The distortion of such Minibrots is not inherited by the respective satellite minibrots. For example the main antenna is bent quite out of shape, but the satellite minibrot there is much closer to symmetrical than the parent.
I had no success trying to "shapestack" distorted minibrots on top of each other. Title: Re: How distorted can a minibrot be? Post by: Adam Majewski on November 13, 2016, 09:00:41 AM Do you know :
http://mrob.com/pub/muency/distortion.html Title: Re: How distorted can a minibrot be? Post by: greentexas on November 16, 2016, 03:10:31 AM Here's some visual evidence showing the convergence to a limit of distortion in elephant valley, with the period doubling each frame: (https://mathr.co.uk/mandelbrot/2016-11-12_warped_midgets.gif) locations: Code: 4 -1.565201668337550811e-01 + 1.032247108922831780e+00 i @ 1.697e-02 The converging seems to be finite. For this reason, I'm guessing the fractal distortion has some sort of "limit". I remember thinking that if you were to zoom into a distorted Minibrot, it would have even more distorted Mandelbrots, and so forth, into complete non-Mandelbrot like shapes. The distorted Mandelbrots do not seem to have heavily distorted zoom-ups, but the parts are rearranged a bit. Title: Re: How distorted can a minibrot be? Post by: Chillheimer on November 16, 2016, 09:30:59 AM I remember thinking that if you were to zoom into a distorted Minibrot, it would have even more distorted Mandelbrots, and so forth, into complete non-Mandelbrot like shapes. Nope, the distortion doesn't 'add up' to the next generation minibrot. The only distortion I ever encountered was in a valley. The deeper, the more distorted.Title: Re: How distorted can a minibrot be? Post by: greentexas on November 16, 2016, 01:31:08 PM You are correct; but that is what I used to think.
Title: Re: How distorted can a minibrot be? Post by: Chillheimer on November 16, 2016, 03:47:55 PM sorry, misread that..
Title: Re: How distorted can a minibrot be? Post by: greentexas on November 16, 2016, 06:04:57 PM Don't worry; it's okay.
Title: Re: How distorted can a minibrot be? Post by: vinecius on October 08, 2017, 09:52:48 AM how is it that i get the same image near (0,0)? at a zoom level of 1 that is 1e0 |