Original file (1,500 × 1,500 pixels, file size: 980 KB, MIME type: image/png )
Summary
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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]
f
c
:
z
→
z
2
+
c
.
{\displaystyle f_{c}:z\to z^{2}+c.\,}
Color of pixel is related to position of
z
8
{\displaystyle z_{8}}
: 8'th iteration of
z
0
{\displaystyle z_{0}}
z
8
=
f
c
8
(
z
0
)
{\displaystyle z_{8}=f_{c}^{8}(z_{0})\,}
where :
z
0
{\displaystyle z_{0}\,}
is current pixel position
c
=
−
3
4
{\displaystyle c=-{\frac {3}{4}}}
n
=
65000
{\displaystyle n=65000}
is maximal number of iterations used for computing Julia set
q
=
8
{\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 :
z
=
2.000000000000000
−
2.000000000000000
i
{\displaystyle z=2.000000000000000-2.000000000000000i}
and
z
=
−
2.000000000000000
+
2.000000000000000
i
{\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
↑ Mandel: software for real and complex dynamics by Wolf Jung
↑ Wikibooks : Fractals : color shows in which quadrant zn lands
↑ Complex quadratic polynomial in wikipedia
↑ wikibooks : plane description
↑ wikibooks : Supersampling
English Add a one-line explanation of what this file represents
File history
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Date/Time Thumbnail Dimensions User Comment
current 22:04, 31 July 2023 1,500 × 1,500 (980 KB) Obscure2020 Optimized with OxiPNG and ZopfliPNG.
10:48, 12 December 2015 1,500 × 1,500 (1.22 MB) Soul windsurfer better quality
08:35, 12 December 2015 1,500 × 1,500 (1.22 MB) Soul windsurfer better quality
18:26, 30 November 2015 640 × 640 (53 KB) Soul windsurfer User created page with UploadWizard
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