File:Mandelbrot Creation Animation.gif
Mandelbrot_Creation_Animation.gif （600 × 600 像素，檔案大小：1.78 MB，MIME 類型：image/gif、循環、20 畫格、20秒）
摘要
| 描述 |
An animated diagram showing iterations of the equation used to generate the Mandelbrot set, a fractal first studied by Benoît Mandelbrot in 1979. The animation shows the values of Z for first 20 iterations of the equation where c is a complex variable. Mandelbrot set graphics are usually generated using the so-called "escape algorithm", where color is assigned according to the number of iterations it took for the equation to diverge past a pre-set limit, and black color is used for regions that never diverge. This, however, is a plot of a much simpler quantity: the actual values of the equation at the first 20 iterations. Every pixel in the image corresponds to a different value of a complex constant c ranging from -2.2 to 1 on the real axis (horizontal) and from -1.2i to 1.2i on the imaginary axis (vertical). Z is initialized to 0. At each iteration, the next value of Z is calculated using the equation above. This graphic was generated with 13 lines of code in the R language (see below for the code). For each point, the magnitude (aka absolute value) of Z is calculated, than scaled using an exponential function to emphasize fine detail, and finally mapped to color palette (jetColors). Dark red is a very low number, dark blue is a very high number. The deep blue region "squeezing" in the boundaries of the fractal is the region where Z value diverges to infinity. |
| 日期 | |
| 來源 | 自己的作品 |
| 作者 | Jarekt |
| 其他版本 |
Mandelbrot Creation Animation (800x600).gif: .gif) |
| GIF開發 | |
| 原始碼 | R codelibrary(caTools)
jet.colors = colorRampPalette(c("#00007F", "blue", "#007FFF", "cyan", "#7FFF7F", "yellow", "#FF7F00", "red", "#7F0000"))
m = 600
C = complex( real=rep(seq(-1.8,0.6, length.out=m), each=m ),
imag=rep(seq(-1.2,1.2, length.out=m), m ) )
C = matrix(C,m,m)
Z = 0
X = array(0, c(m,m,20))
for (k in 1:20) {
Z = Z^2+C
X[,,k] = exp(-abs(Z))
}
write.gif(X, "Mandelbrot.gif", col=jet.colors, delay=100)
|
授權條款
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已授權您依據自由軟體基金會發行的無固定段落、封面文字和封底文字GNU自由文件授權條款1.2版或任意後續版本，對本檔進行複製、傳播和／或修改。該協議的副本列在GNU自由文件授權條款中。 |
檔案歷史
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| 日期/時間 | 縮圖 | 尺寸 | 使用者 | 備註 | |
|---|---|---|---|---|---|
| 目前 | 2007年6月13日 (三) 18:32 | | 600 × 600（1.78 MB） | Jarekt | {{Information |Description=Animation GIF file showing iteration of creating Mandelbrot set image |Source=self-made |Date=06/13/2007 |Author= Jarekt }} Image generated using R language and executing the following code: library(caTools) jet |
檔案用途
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- cs.wikipedia.org 的使用狀況
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- fa.wikipedia.org 的使用狀況
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- kn.wikipedia.org 的使用狀況
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- pt.wikipedia.org 的使用狀況
