Summary

Licensing

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

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You are free:

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• to remix – to adapt the work

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

Summary

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 ${\displaystyle z=-2.000000000000000+2.000000000000000i}$

Image Magic src code

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],

References

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