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C# 绘制Mandelbrot集合图像
C# 绘制Mandelbrot集合图像
关于MandelbrotSet的定义,可以参考英文版维基百科条目 Mandelbrot Set
本程序是一个单窗体程序,里面只有一个PictureBox控件pcbMS,用于放置绘制好的图像
一、23次迭代的黑白版本
1)生成图像
2)程序源码
using System; using System.Collections.Generic; using System.ComponentModel; using System.Data; using System.Drawing; using System.Linq; using System.Text; using System.Threading.Tasks; using System.Windows.Forms; namespace MandelbrotSet { public partial class FormMain : Form { public FormMain() { InitializeComponent(); } private void FormMain_Load(object sender, EventArgs e) { //建立新的Image pcbMS.Image = new Bitmap(pcbMS.Width, pcbMS.Height); //计算各点的等级 int[,] temp = PointSet(23); //生成新的Bitmap,并设置各点颜色 Bitmap bmpTemp = new Bitmap(pcbMS.Width, pcbMS.Height); for (int i = 0; i < bmpTemp.Width; i++) { for (int j = 0; j < bmpTemp.Height; j++) { bmpTemp.SetPixel(i, j, GetColor(temp[i, j])); } } //赋值到PictureBox的Image上 pcbMS.Image = bmpTemp; } /// <summary> /// 根据迭代次数分配颜色 /// </summary> /// <param name="i"></param> /// <returns></returns> Color GetColor(int i) { return i == 0 ? Color.White : Color.Black; } //复数结构 public struct Complex { public double Real; //实部 public double Imag; //虚部 /// <summary> /// 建立一个复数 x+yi /// </summary> /// <param name="x">实部</param> /// <param name="y">虚部</param> public Complex(double x, double y) { Real = x; Imag = y; } /// <summary> /// 调整图形在窗口中的位置 /// </summary> /// <param name="a">原实部位置</param> /// <param name="b">原虚部位置</param> /// <returns>调整后的位置</returns> public static Complex Converse(double a, double b) { return new Complex(a / 380.0 - 2.4, b / 280.0 - 1.25); } } /// <summary> /// 点集求值 /// </summary> /// <param name="maxiter">最大迭代次数</param> /// <returns>求值后的集合</returns> int[,] PointSet(int maxiter = 7) { int[,] MSet = new int[pcbMS.Width, pcbMS.Height]; var iter = 0; var current = new Complex(0.0, 0.0); var temp = new Complex(0.0, 0.0); for (int x = 0; x < pcbMS.Width; x++) { for (int y = 0; y < pcbMS.Height; y++) { iter = 0; current = Complex.Converse(x, y); temp = current; while (temp.Real*temp.Real + temp.Imag*temp.Imag <= 4 && iter < maxiter) { temp = new Complex( temp.Real * temp.Real - temp.Imag * temp.Imag + current.Real, 2 * temp.Real * temp.Imag + current.Imag); iter = iter + 1; } MSet[x, y] = iter == maxiter ? 1 : 0; } } return MSet; } } }
一、23次迭代的彩色版本
1)生成图像
2)程序源码
using System; using System.Collections.Generic; using System.ComponentModel; using System.Data; using System.Drawing; using System.Linq; using System.Text; using System.Threading.Tasks; using System.Windows.Forms; namespace MandelbrotSet { public partial class FormMain : Form { public FormMain() { InitializeComponent(); } private void FormMain_Load(object sender, EventArgs e) { //建立新的Image pcbMS.Image = new Bitmap(pcbMS.Width, pcbMS.Height); //计算各点的等级 int[,] temp = PointSet(23); //生成新的Bitmap,并设置各点颜色 Bitmap bmpTemp = new Bitmap(pcbMS.Width, pcbMS.Height); for (int i = 0; i < bmpTemp.Width; i++) { for (int j = 0; j < bmpTemp.Height; j++) { bmpTemp.SetPixel(i, j, GetColor(temp[i, j])); } } //赋值到PictureBox的Image上 pcbMS.Image = bmpTemp; } /// <summary> /// 根据迭代次数分配颜色 /// </summary> /// <param name="i"></param> /// <returns></returns> Color GetColor(int i) { switch (i % 8) { case 0: return Color.Red; case 1: return Color.Orange; case 2: return Color.Yellow; case 3: return Color.Green; case 4: return Color.Cyan; case 5: return Color.Blue; case 6: return Color.Purple; case 7: return Color.Black; default: return Color.Black; } } //复数结构 public struct Complex { public double Real; //实部 public double Imag; //虚部 /// <summary> /// 建立一个复数 x+yi /// </summary> /// <param name="x">实部</param> /// <param name="y">虚部</param> public Complex(double x, double y) { Real = x; Imag = y; } /// <summary> /// 调整图形在窗口中的位置 /// </summary> /// <param name="a">原实部位置</param> /// <param name="b">原虚部位置</param> /// <returns>调整后的位置</returns> public static Complex Converse(double a, double b) { return new Complex(a / 380.0 - 2.4, b / 280.0 - 1.25); } } /// <summary> /// 点集求值 /// </summary> /// <param name="maxiter">最大迭代次数</param> /// <returns>求值后的集合</returns> int[,] PointSet(int maxiter = 7) { int[,] MSet = new int[pcbMS.Width, pcbMS.Height]; var iter = 0; var current = new Complex(0.0, 0.0); var temp = new Complex(0.0, 0.0); for (int x = 0; x < pcbMS.Width; x++) { for (int y = 0; y < pcbMS.Height; y++) { iter = 0; current = Complex.Converse(x, y); temp = current; while (temp.Real*temp.Real + temp.Imag*temp.Imag <= 4 && iter < maxiter) { temp = new Complex( temp.Real * temp.Real - temp.Imag * temp.Imag + current.Real, 2 * temp.Real * temp.Imag + current.Imag); iter = iter + 1; } MSet[x, y] = iter; } } return MSet; } } }
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C# 绘制Mandelbrot集合图像
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