我想使用 Java 生成 Mandelbrot 集的 PNG 照片，輸出應(yīng)該很容易在谷歌圖像搜索中找到。該集合定義為以下序列：z_n+1 = z_n^2 + c其中c和z是復(fù)數(shù)，并且z始終具有小于 2 的模數(shù)。我首先為復(fù)數(shù)定義了一個(gè)類，其中還包含所需的基本復(fù)雜運(yùn)算。public class ComplexNumber { private double real; private double imaginary; public ComplexNumber(double real, double imaginary) { this.real = real; this.imaginary = imaginary; } public ComplexNumber add(ComplexNumber z1, ComplexNumber z2) { ComplexNumber sum = new ComplexNumber(0, 0); sum.real = z1.real + z2.real; sum.imaginary = z1.imaginary + z2.imaginary; return sum; } public ComplexNumber square(ComplexNumber z) { ComplexNumber squared = new ComplexNumber(0, 0); squared.real = Math.pow(z.real, 2) - Math.pow(z.imaginary, 2); squared.imaginary = 2 * z.real * z.imaginary; return squared; } public double abs() { double absolute = Math.sqrt(Math.pow(this.real, 2) + Math.pow(this.imaginary, 2)); return absolute; }}然后我定義了 Mandelbrot 類，它獲取許多復(fù)數(shù) c（基于像素）檢查這些數(shù)字是否在使用 mandelbrot 方法的 mandelbrot 集中，并將此方法的輸出轉(zhuǎn)換為要顯示的顏色。import java.awt.image.BufferedImage;import java.io.File;import java.io.IOException;import javax.imageio.ImageIO;public class Mandelbrot { public static int mandelbrot(ComplexNumber c, ComplexNumber z, int i, int n) { if (i < n) { if (c.abs() > 2.0) { return i; } else return 0; } return mandelbrot(c, z.square(z).add(z, c), i, n); }
1 回答
慕標(biāo)琳琳
TA貢獻(xiàn)1830條經(jīng)驗(yàn) 獲得超9個(gè)贊
看起來(lái)您的遞歸 mandelbrot 函數(shù)的終止條件不正確。
您希望 mandelbrot 函數(shù)返回，當(dāng)
z 的絕對(duì)值超過(guò) 2 或
達(dá)到最大遞歸深度。
另外，你永遠(yuǎn)不會(huì)增加 i。
所以更新后的函數(shù)看起來(lái)像：
public static int mandelbrot(ComplexNumber c, ComplexNumber z, int i, int n) {
if (i >= n) {
// mandelbrot function does not diverge after n iterations.
// Returning -1 as a magic value to indicate that the point c is in the mandelbrot set.
// Values may already be outside of the mandelbrot set in the 0th iteration, so returning -1 makes more sense.
return -1;
} else if (z.abs() >= 2.0) {
// mandelbrot function is diverging after i iterations.
return i;
} else {
// recursively call mandelbrot function with an updated z and an incremented i.
return mandelbrot(c, z.squared().add(c), i + 1, n);
}
}
最后，如果您選擇為 mandelbrot 集中的某個(gè)點(diǎn)返回 -1，則必須更新您的顏色計(jì)算以將這些點(diǎn)設(shè)置為黑色。
int mb = mandelbrot(c, z0, 0, maxRecurse);
if (mb == -1) {
image.setRGB(x, y, 0);
} else {
// set the color of your image as usual
}
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