I, the copyright holder of this work, hereby publish it under the following license:

This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.

You are free:

• to share – to copy, distribute and transmit the work
• to remix – to adapt the work

Under the following conditions:

• attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
• share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

https://creativecommons.org/licenses/by-sa/4.0CC BY-SA 4.0 Creative Commons Attribution-Share Alike 4.0 truetrue

This image :

• is made by the program Mandel^[1] by Wolf Jung ( algorithm 9 = zeros of qn(c) ) ^[2]
• shows rectangle part of dynamic plane of discrete dynamical system based on complex quadratic polynomial )( map )^[3]

${\displaystyle f_{c}:z\to z^{2}+c.\,}$

Color of pixel is related to position of ${\displaystyle z_{8}}$ : 8'th iteration of ${\displaystyle z_{0}}$

${\displaystyle z_{8}=f_{c}^{8}(z_{0})\,}$

where :

• ${\displaystyle z_{0}\,}$ is current pixel position
• ${\displaystyle c=-{\frac {3}{4}}}$
• ${\displaystyle n=65000}$ is maximal number of iterations used for computing Julia set
• ${\displaystyle q=8}$ is number of iterations used for algorithm 9
• size of image is 8000 pixels ( use F5 or menu ). It is maximal value for the program
• corners^[4] of rectangle are : ${\displaystyle z=2.000000000000000-2.000000000000000i}$ and ${\displaystyle z=-2.000000000000000+2.000000000000000i}$

Big image ( 8000x8000 pixels give 1.9 MB ) is downsized using Image Magic console tool :

convert d.png -resize 1500x1500 dasmall.png

It gives :

• smaller size
• bette quality ( subpixel accuracy )^[5],

1. ↑ Mandel: software for real and complex dynamics by Wolf Jung
2. ↑ Wikibooks : Fractals : color shows in which quadrant zn lands
3. ↑ Complex quadratic polynomial in wikipedia
4. ↑ wikibooks : plane description
5. ↑ wikibooks : Supersampling