File:Points on dynamical parabolic planes.png
![File:Points on dynamical parabolic planes.png](https://upload.wikimedia.org/wikipedia/commons/thumb/9/96/Points_on_dynamical_parabolic_planes.png/420px-Points_on_dynamical_parabolic_planes.png?20150202201231)
Original file (504 × 720 pixels, file size: 5 KB, MIME type: image/png)
Captions
Captions
Contents
Summary
[edit]DescriptionPoints on dynamical parabolic planes.png |
English: This diagram shows changes on dynamic plane for fc(z)= z^2 + c when c = -0.75 ( parabolic parameter) |
Date | |
Source | Own work |
Author | Adam majewski |
Licensing
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Summary
[edit]![](https://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Discrete_dynamic_in_case_of_complex_quadratic_polynomial.gif/220px-Discrete_dynamic_in_case_of_complex_quadratic_polynomial.gif)
Components
[edit]From math point of view there are :
Fatou set consist of components ( subsets) :
- attracting components ( here exterior of Julia set )
- parabolic compoent ) here interior of Julia set )
From programming point of view ( because of numerical methods and limited precision ) there are 3 components of image :
- known exterior = escaping set, all pixels that escape to infinity
- known interior = attracting set, all pixels which are attracted by alfa fixed point after limited iterations ( Max iter )
- unknown pixels, all pixels which do not escape or not attracted by alfa fixed point after limited iterations ( Max iter )
Sets | color | description |
---|---|---|
escaping set | white ( light gray ) | |
attracting set | dark gray | |
unknown | red | |
Julia set | black | not seen on this image |
Data.text file
[edit]# maxiter ExteriorPixels InteriorPixels UnknownPixesl 0 0.000000 0.000234 0.999766 1 0.328092 0.000477 0.671431 2 0.547592 0.000575 0.451833 3 0.640913 0.000653 0.358433 4 0.687845 0.000693 0.311461 5 0.714504 0.000721 0.284775 6 0.730709 0.000741 0.268549 7 0.741129 0.000757 0.258113 8 0.748003 0.000765 0.251232 9 0.752817 0.000772 0.246411 10 0.756136 0.000776 0.243088 11 0.758540 0.000780 0.240680 12 0.760269 0.000785 0.238945 13 0.761567 0.000788 0.237645 14 0.762573 0.000788 0.236639 15 0.763303 0.000789 0.235908 16 0.763921 0.000789 0.235289 17 0.764345 0.000791 0.234864 18 0.764708 0.000792 0.234500 19 0.765025 0.000792 0.234183 ...
Gnuplot src code
[edit]set terminal postscript portrait enhanced mono dashed lw 1 "Helvetica" 14
set output "data1.ps"
set title "Points on dynamical plane "
set ylabel "ratio"
set xlabel "iteratio max"
#set xrange [0:150]
# define styles
#set style data lines
set style line 1 lc rgb "green" lt 1 lw 5 pt 1 ps 1.5 #
set style line 2 lc rgb "blue" lt 1 lw 5 pt 1 ps 1.5 #
set style line 3 lc rgb "red" lt 1 lw 5 pt 1 ps 1.5 #
# plot "data.txt" using 1:2 title 'exterior' lc 1, "data.txt" using 1:3 title 'interior' lc 2, "data.txt" using 1:4 title 'unknown' lc 3
# plot "data.txt" using 1:2 title 'exterior' with linespoints ls 1, "data.txt" using 1:3 title 'interior' with linespoints ls 2, "data.txt" using 1:4 title 'unknown' with linespoints ls 3
# To reuse the last filename we can just type ""
# plot "data.txt" using 1:2 title 'exterior' with linespoints ls 1, "" using 1:3 title 'interior' with linespoints ls 2, "" using 1:4 title 'unknown' with linespoints ls 3
plot "data.txt" using 1:2 title 'exterior' with lines ls 1, "" using 1:3 title 'interior' with lines ls 2, "" using 1:4 title 'unknown' with lines ls 3
References
[edit]File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 20:12, 2 February 2015 | ![]() | 504 × 720 (5 KB) | Soul windsurfer (talk | contribs) | computed with the same parameters ( size) |
19:40, 2 February 2015 | ![]() | 504 × 720 (6 KB) | Soul windsurfer (talk | contribs) | User created page with UploadWizard |
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Horizontal resolution | 28.35 dpc |
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Vertical resolution | 28.35 dpc |
File change date and time | 20:11, 2 February 2015 |