// Fraktale Newtona
// www.algorytm.org
// Tomasz Lubinski (c) 2009

using System;
using System.Drawing;
using System.Collections;
using System.ComponentModel;
using System.Windows.Forms;
using System.Data;

namespace Newton
{
	/// <summary>
	/// Fraktale Newtona
	/// www.algorytm.org
	/// Tomasz Lubinski (c) 2006
	/// </summary>
	public class Form1 : System.Windows.Forms.Form
	{
		private System.Windows.Forms.Button button1;
		private System.Windows.Forms.Label label2;
		private System.Windows.Forms.TextBox maxy;
		private System.Windows.Forms.TextBox miny;
		private System.Windows.Forms.Label label1;
		private System.Windows.Forms.TextBox maxx;
		private System.Windows.Forms.TextBox minx;
		private System.Windows.Forms.PictureBox Fractal;
		private Graphics graph;

		//Describes places to render
		private double ratioX;
		private double ratioY;
		private double minX;
		private double minY;
		private double maxX;
		private double maxY;
		private int downX;
		private int downY;

		//Describes sets to color
		private complex_t [] results = new complex_t[10];
		private int resultsCnt;
		private bool cSet;

		private Pen [] penColors = new Pen[100];
		private System.Windows.Forms.Panel Selection;
		private System.Windows.Forms.Button button2;
		private System.Windows.Forms.Label label3;
		private System.Windows.Forms.Label label4;
		private System.Windows.Forms.Label label5;
		private System.Windows.Forms.TextBox aIm;
		private System.Windows.Forms.TextBox aRe;
		private System.Windows.Forms.Label label6;
		private System.Windows.Forms.Label label7;
		private System.Windows.Forms.Label label8;
		private System.Windows.Forms.Label label9;
		private System.Windows.Forms.Label label10;
		private System.Windows.Forms.Label label11;
		private System.Windows.Forms.Label label12;
		private System.Windows.Forms.Label label13;
		private System.Windows.Forms.Label label14;
		private System.Windows.Forms.RadioButton colorSpeed;
		private System.Windows.Forms.RadioButton colorSet;
		private System.Windows.Forms.TextBox pr0;
		private System.Windows.Forms.TextBox pi0;
		private System.Windows.Forms.TextBox pi1;
		private System.Windows.Forms.TextBox pr1;
		private System.Windows.Forms.TextBox pi2;
		private System.Windows.Forms.TextBox pr2;
		private System.Windows.Forms.TextBox pi3;
		private System.Windows.Forms.TextBox pr3;
		private System.Windows.Forms.TextBox pi4;
		private System.Windows.Forms.TextBox pr4;
		private System.Windows.Forms.TextBox pi5;
		private System.Windows.Forms.TextBox pr5;

		/// <summary>
		/// Required designer variable.
		/// </summary>
		private System.ComponentModel.Container components = null;

		public Form1()
		{
			//
			// Required for Windows Form Designer support
			//
			InitializeComponent();
		}

		/// <summary>
		/// Clean up any resources being used.
		/// </summary>
		protected override void Dispose( bool disposing )
		{
			if( disposing )
			{
				if (components != null) 
				{
					components.Dispose();
				}
			}
			base.Dispose( disposing );
		}

		#region Windows Form Designer generated code
		/// <summary>
		/// Required method for Designer support - do not modify
		/// the contents of this method with the code editor.
		/// </summary>
		private void InitializeComponent()
		{
			this.button1 = new System.Windows.Forms.Button();
			this.label2 = new System.Windows.Forms.Label();
			this.maxy = new System.Windows.Forms.TextBox();
			this.miny = new System.Windows.Forms.TextBox();
			this.label1 = new System.Windows.Forms.Label();
			this.maxx = new System.Windows.Forms.TextBox();
			this.minx = new System.Windows.Forms.TextBox();
			this.Fractal = new System.Windows.Forms.PictureBox();
			this.Selection = new System.Windows.Forms.Panel();
			this.button2 = new System.Windows.Forms.Button();
			this.label3 = new System.Windows.Forms.Label();
			this.aIm = new System.Windows.Forms.TextBox();
			this.aRe = new System.Windows.Forms.TextBox();
			this.label4 = new System.Windows.Forms.Label();
			this.label5 = new System.Windows.Forms.Label();
			this.label6 = new System.Windows.Forms.Label();
			this.label7 = new System.Windows.Forms.Label();
			this.label8 = new System.Windows.Forms.Label();
			this.pr0 = new System.Windows.Forms.TextBox();
			this.pi0 = new System.Windows.Forms.TextBox();
			this.pi1 = new System.Windows.Forms.TextBox();
			this.pr1 = new System.Windows.Forms.TextBox();
			this.pi2 = new System.Windows.Forms.TextBox();
			this.pr2 = new System.Windows.Forms.TextBox();
			this.pi3 = new System.Windows.Forms.TextBox();
			this.pr3 = new System.Windows.Forms.TextBox();
			this.pi4 = new System.Windows.Forms.TextBox();
			this.pr4 = new System.Windows.Forms.TextBox();
			this.pi5 = new System.Windows.Forms.TextBox();
			this.pr5 = new System.Windows.Forms.TextBox();
			this.label9 = new System.Windows.Forms.Label();
			this.label10 = new System.Windows.Forms.Label();
			this.label11 = new System.Windows.Forms.Label();
			this.label12 = new System.Windows.Forms.Label();
			this.label13 = new System.Windows.Forms.Label();
			this.label14 = new System.Windows.Forms.Label();
			this.colorSpeed = new System.Windows.Forms.RadioButton();
			this.colorSet = new System.Windows.Forms.RadioButton();
			this.SuspendLayout();
			// 
			// button1
			// 
			this.button1.Location = new System.Drawing.Point(392, 408);
			this.button1.Name = "button1";
			this.button1.TabIndex = 15;
			this.button1.Text = "Generuj";
			this.button1.Click += new System.EventHandler(this.button1_Click);
			// 
			// label2
			// 
			this.label2.Location = new System.Drawing.Point(376, 72);
			this.label2.Name = "label2";
			this.label2.Size = new System.Drawing.Size(64, 23);
			this.label2.TabIndex = 14;
			this.label2.Text = "Zakres Y";
			// 
			// maxy
			// 
			this.maxy.Location = new System.Drawing.Point(440, 96);
			this.maxy.Name = "maxy";
			this.maxy.Size = new System.Drawing.Size(120, 20);
			this.maxy.TabIndex = 13;
			this.maxy.Text = "textBox3";
			// 
			// miny
			// 
			this.miny.Location = new System.Drawing.Point(440, 72);
			this.miny.Name = "miny";
			this.miny.Size = new System.Drawing.Size(120, 20);
			this.miny.TabIndex = 12;
			this.miny.Text = "textBox4";
			// 
			// label1
			// 
			this.label1.Location = new System.Drawing.Point(376, 17);
			this.label1.Name = "label1";
			this.label1.Size = new System.Drawing.Size(64, 23);
			this.label1.TabIndex = 11;
			this.label1.Text = "Zakres X";
			// 
			// maxx
			// 
			this.maxx.Location = new System.Drawing.Point(440, 41);
			this.maxx.Name = "maxx";
			this.maxx.Size = new System.Drawing.Size(120, 20);
			this.maxx.TabIndex = 10;
			this.maxx.Text = "textBox2";
			// 
			// minx
			// 
			this.minx.Location = new System.Drawing.Point(440, 17);
			this.minx.Name = "minx";
			this.minx.Size = new System.Drawing.Size(120, 20);
			this.minx.TabIndex = 9;
			this.minx.Text = "textBox1";
			// 
			// Fractal
			// 
			this.Fractal.Cursor = System.Windows.Forms.Cursors.Cross;
			this.Fractal.Location = new System.Drawing.Point(8, 8);
			this.Fractal.Name = "Fractal";
			this.Fractal.Size = new System.Drawing.Size(352, 352);
			this.Fractal.TabIndex = 8;
			this.Fractal.TabStop = false;
			this.Fractal.MouseUp += new System.Windows.Forms.MouseEventHandler(this.Fractal_MouseUp);
			this.Fractal.MouseMove += new System.Windows.Forms.MouseEventHandler(this.Fractal_MouseMove);
			this.Fractal.MouseDown += new System.Windows.Forms.MouseEventHandler(this.Fractal_MouseDown);
			// 
			// Selection
			// 
			this.Selection.BackColor = System.Drawing.SystemColors.HighlightText;
			this.Selection.Location = new System.Drawing.Point(160, 160);
			this.Selection.Name = "Selection";
			this.Selection.Size = new System.Drawing.Size(48, 40);
			this.Selection.TabIndex = 16;
			this.Selection.Visible = false;
			// 
			// button2
			// 
			this.button2.Location = new System.Drawing.Point(480, 408);
			this.button2.Name = "button2";
			this.button2.TabIndex = 17;
			this.button2.Text = "Reset";
			this.button2.Click += new System.EventHandler(this.Form1_Load);
			// 
			// label3
			// 
			this.label3.Location = new System.Drawing.Point(16, 368);
			this.label3.Name = "label3";
			this.label3.Size = new System.Drawing.Size(184, 48);
			this.label3.TabIndex = 18;
			this.label3.Text = "W oknie po lewej zaznacz fragment do powiekszenia, badz wpisz  zakres recznie i n" +
				"acisnij \"Generuj\"";
			// 
			// aIm
			// 
			this.aIm.Location = new System.Drawing.Point(440, 152);
			this.aIm.Name = "aIm";
			this.aIm.Size = new System.Drawing.Size(120, 20);
			this.aIm.TabIndex = 20;
			this.aIm.Text = "textBox3";
			// 
			// aRe
			// 
			this.aRe.Location = new System.Drawing.Point(440, 128);
			this.aRe.Name = "aRe";
			this.aRe.Size = new System.Drawing.Size(120, 20);
			this.aRe.TabIndex = 19;
			this.aRe.Text = "textBox4";
			// 
			// label4
			// 
			this.label4.Location = new System.Drawing.Point(400, 136);
			this.label4.Name = "label4";
			this.label4.Size = new System.Drawing.Size(40, 23);
			this.label4.TabIndex = 21;
			this.label4.Text = "a (Re)";
			// 
			// label5
			// 
			this.label5.Location = new System.Drawing.Point(400, 160);
			this.label5.Name = "label5";
			this.label5.Size = new System.Drawing.Size(40, 23);
			this.label5.TabIndex = 22;
			this.label5.Text = "a (Im)";
			// 
			// label6
			// 
			this.label6.Location = new System.Drawing.Point(376, 184);
			this.label6.Name = "label6";
			this.label6.Size = new System.Drawing.Size(40, 23);
			this.label6.TabIndex = 23;
			this.label6.Text = "n";
			// 
			// label7
			// 
			this.label7.Location = new System.Drawing.Point(424, 184);
			this.label7.Name = "label7";
			this.label7.Size = new System.Drawing.Size(48, 23);
			this.label7.TabIndex = 24;
			this.label7.Text = "p(Re)^n";
			// 
			// label8
			// 
			this.label8.Location = new System.Drawing.Point(496, 184);
			this.label8.Name = "label8";
			this.label8.Size = new System.Drawing.Size(56, 23);
			this.label8.TabIndex = 25;
			this.label8.Text = "p(Im)^n";
			// 
			// pr0
			// 
			this.pr0.Location = new System.Drawing.Point(408, 208);
			this.pr0.Name = "pr0";
			this.pr0.Size = new System.Drawing.Size(72, 20);
			this.pr0.TabIndex = 26;
			this.pr0.Text = "textBox3";
			// 
			// pi0
			// 
			this.pi0.Location = new System.Drawing.Point(488, 208);
			this.pi0.Name = "pi0";
			this.pi0.Size = new System.Drawing.Size(72, 20);
			this.pi0.TabIndex = 27;
			this.pi0.Text = "textBox3";
			// 
			// pi1
			// 
			this.pi1.Location = new System.Drawing.Point(488, 232);
			this.pi1.Name = "pi1";
			this.pi1.Size = new System.Drawing.Size(72, 20);
			this.pi1.TabIndex = 29;
			this.pi1.Text = "textBox3";
			// 
			// pr1
			// 
			this.pr1.Location = new System.Drawing.Point(408, 232);
			this.pr1.Name = "pr1";
			this.pr1.Size = new System.Drawing.Size(72, 20);
			this.pr1.TabIndex = 28;
			this.pr1.Text = "textBox3";
			// 
			// pi2
			// 
			this.pi2.Location = new System.Drawing.Point(488, 256);
			this.pi2.Name = "pi2";
			this.pi2.Size = new System.Drawing.Size(72, 20);
			this.pi2.TabIndex = 31;
			this.pi2.Text = "textBox3";
			// 
			// pr2
			// 
			this.pr2.Location = new System.Drawing.Point(408, 256);
			this.pr2.Name = "pr2";
			this.pr2.Size = new System.Drawing.Size(72, 20);
			this.pr2.TabIndex = 30;
			this.pr2.Text = "textBox3";
			// 
			// pi3
			// 
			this.pi3.Location = new System.Drawing.Point(488, 280);
			this.pi3.Name = "pi3";
			this.pi3.Size = new System.Drawing.Size(72, 20);
			this.pi3.TabIndex = 33;
			this.pi3.Text = "textBox3";
			// 
			// pr3
			// 
			this.pr3.Location = new System.Drawing.Point(408, 280);
			this.pr3.Name = "pr3";
			this.pr3.Size = new System.Drawing.Size(72, 20);
			this.pr3.TabIndex = 32;
			this.pr3.Text = "textBox3";
			// 
			// pi4
			// 
			this.pi4.Location = new System.Drawing.Point(488, 304);
			this.pi4.Name = "pi4";
			this.pi4.Size = new System.Drawing.Size(72, 20);
			this.pi4.TabIndex = 35;
			this.pi4.Text = "textBox3";
			// 
			// pr4
			// 
			this.pr4.Location = new System.Drawing.Point(408, 304);
			this.pr4.Name = "pr4";
			this.pr4.Size = new System.Drawing.Size(72, 20);
			this.pr4.TabIndex = 34;
			this.pr4.Text = "textBox3";
			// 
			// pi5
			// 
			this.pi5.Location = new System.Drawing.Point(488, 328);
			this.pi5.Name = "pi5";
			this.pi5.Size = new System.Drawing.Size(72, 20);
			this.pi5.TabIndex = 37;
			this.pi5.Text = "textBox3";
			// 
			// pr5
			// 
			this.pr5.Location = new System.Drawing.Point(408, 328);
			this.pr5.Name = "pr5";
			this.pr5.Size = new System.Drawing.Size(72, 20);
			this.pr5.TabIndex = 36;
			this.pr5.Text = "textBox3";
			// 
			// label9
			// 
			this.label9.Location = new System.Drawing.Point(376, 210);
			this.label9.Name = "label9";
			this.label9.Size = new System.Drawing.Size(16, 23);
			this.label9.TabIndex = 38;
			this.label9.Text = "0";
			// 
			// label10
			// 
			this.label10.Location = new System.Drawing.Point(376, 232);
			this.label10.Name = "label10";
			this.label10.Size = new System.Drawing.Size(16, 23);
			this.label10.TabIndex = 39;
			this.label10.Text = "1";
			// 
			// label11
			// 
			this.label11.Location = new System.Drawing.Point(376, 256);
			this.label11.Name = "label11";
			this.label11.Size = new System.Drawing.Size(16, 23);
			this.label11.TabIndex = 40;
			this.label11.Text = "2";
			// 
			// label12
			// 
			this.label12.Location = new System.Drawing.Point(376, 280);
			this.label12.Name = "label12";
			this.label12.Size = new System.Drawing.Size(16, 23);
			this.label12.TabIndex = 41;
			this.label12.Text = "3";
			// 
			// label13
			// 
			this.label13.Location = new System.Drawing.Point(376, 304);
			this.label13.Name = "label13";
			this.label13.Size = new System.Drawing.Size(16, 23);
			this.label13.TabIndex = 42;
			this.label13.Text = "4";
			// 
			// label14
			// 
			this.label14.Location = new System.Drawing.Point(376, 328);
			this.label14.Name = "label14";
			this.label14.Size = new System.Drawing.Size(16, 23);
			this.label14.TabIndex = 43;
			this.label14.Text = "5";
			// 
			// colorSpeed
			// 
			this.colorSpeed.Checked = true;
			this.colorSpeed.Location = new System.Drawing.Point(384, 360);
			this.colorSpeed.Name = "colorSpeed";
			this.colorSpeed.Size = new System.Drawing.Size(176, 16);
			this.colorSpeed.TabIndex = 44;
			this.colorSpeed.TabStop = true;
			this.colorSpeed.Text = "Koloruj szybkosc przyciagania";
			// 
			// colorSet
			// 
			this.colorSet.Location = new System.Drawing.Point(384, 384);
			this.colorSet.Name = "colorSet";
			this.colorSet.Size = new System.Drawing.Size(176, 16);
			this.colorSet.TabIndex = 45;
			this.colorSet.Text = "Koloruj zbior rozwiazania";
			// 
			// Form1
			// 
			this.AutoScaleBaseSize = new System.Drawing.Size(5, 13);
			this.ClientSize = new System.Drawing.Size(568, 443);
			this.Controls.Add(this.colorSet);
			this.Controls.Add(this.colorSpeed);
			this.Controls.Add(this.label14);
			this.Controls.Add(this.label13);
			this.Controls.Add(this.label12);
			this.Controls.Add(this.label11);
			this.Controls.Add(this.label10);
			this.Controls.Add(this.label9);
			this.Controls.Add(this.pi5);
			this.Controls.Add(this.pr5);
			this.Controls.Add(this.pi4);
			this.Controls.Add(this.pr4);
			this.Controls.Add(this.pi3);
			this.Controls.Add(this.pr3);
			this.Controls.Add(this.pi2);
			this.Controls.Add(this.pr2);
			this.Controls.Add(this.pi1);
			this.Controls.Add(this.pr1);
			this.Controls.Add(this.pi0);
			this.Controls.Add(this.pr0);
			this.Controls.Add(this.label8);
			this.Controls.Add(this.label7);
			this.Controls.Add(this.label6);
			this.Controls.Add(this.label5);
			this.Controls.Add(this.label4);
			this.Controls.Add(this.aIm);
			this.Controls.Add(this.aRe);
			this.Controls.Add(this.label3);
			this.Controls.Add(this.button2);
			this.Controls.Add(this.Selection);
			this.Controls.Add(this.button1);
			this.Controls.Add(this.label2);
			this.Controls.Add(this.maxy);
			this.Controls.Add(this.miny);
			this.Controls.Add(this.label1);
			this.Controls.Add(this.maxx);
			this.Controls.Add(this.minx);
			this.Controls.Add(this.Fractal);
			this.Name = "Form1";
			this.Text = "Fraktale Newtona - www.algorytm.org (c) 2009 by Tomasz Lubinski";
			this.Load += new System.EventHandler(this.Form1_Load);
			this.ResumeLayout(false);

		}
		#endregion

		/// <summary>
		/// The main entry point for the application.
		/// </summary>
		[STAThread]
		static void Main() 
		{
			Application.Run(new Form1());
		}

		//for HSV colors
		private void HSV2RGB(float hue, float sat, float val, out float red, out float grn, out float blu)
		{
			int i;
			float f, p, q, t;
			red=0; grn=0; blu=0;
			if(val==0) {return;}
			else
			{
				hue/=60;
				i = (int)(hue);
				f = hue-i;
				p = val*(1-sat);
				q = val*(1-(sat*f));
				t = val*(1-(sat*(1-f)));
				if (i==0) {red=val; grn=t; blu=p;}
				else if (i==1) {red=q; grn=val; blu=p;}
				else if (i==2) {red=p; grn=val; blu=t;}
				else if (i==3) {red=p; grn=q; blu=val;}
				else if (i==4) {red=t; grn=p; blu=val;}
				else if (i==5) {red=val; grn=p; blu=q;}
			}
		}

		//initialize color pens
		private void initializeColors()
		{
			float r, g, b;

			for (int i=0; i<penColors.Length-1; i++)
			{
				HSV2RGB((float)2.5*i, (float)0.85, (float)0.8, out r, out g, out b);
				penColors[i] = new Pen(Color.FromArgb((int)(r*255), (int)(g*255), (int)(b*255)));
			}
			penColors[penColors.Length-1] = new Pen(Color.FromArgb(0, 0, 0));
		}

		//complex addition
		private complex_t add(complex_t a, complex_t b)
		{
			complex_t result = new complex_t();

			result.real =  a.real + b.real;
			result.imaginary = a.imaginary + b.imaginary;

			return result;
		}

		//complex substraction
		private complex_t sub(complex_t a, complex_t b)
		{
			complex_t result = new complex_t();

			result.real =  a.real - b.real;
			result.imaginary = a.imaginary - b.imaginary;

			return result;
		}


		//complex multiplication
		private complex_t mul(complex_t a, complex_t b)
		{
			complex_t result = new complex_t();

			result.real =  a.real*b.real - a.imaginary*b.imaginary;
			result.imaginary = a.real*b.imaginary + a.imaginary*b.real;

			return result;
		}

		//complex divide
		private complex_t div(complex_t a, complex_t b)
		{
			complex_t result = new complex_t();
			double x = b.real*b.real + b.imaginary*b.imaginary;

			result.real =  (a.real*b.real + a.imaginary*b.imaginary) / x;
			result.imaginary = (a.imaginary*b.real - a.real*b.imaginary) / x;

			return result;
		}

		//func = a[0] + a[1]*z^1 + a[2]*z^2 + ... a[n]*z^2
		private complex_t func(complex_t z, complex_t [] a)
		{
			int i;
			complex_t result = new complex_t();

			result.real = 0;
			result.imaginary = 0;

			for (i=a.Length-1; i>=0; i--)
			{
				result = add(a[i], mul(result, z));
			}

			return result;
		}

		private int findResult(complex_t a)
		{
			int i;
        
			for (i=0; i<resultsCnt; i++)
			{
				if (sub(a, results[i]).complexModSq() < 0.1)
				{
					return i+1;
				}
			}

			results[resultsCnt] = a;
			resultsCnt++;
			return resultsCnt;
		}

		/// <summary>
		/// Generates newton's fractal
		/// </summary>
		/// <param name="sender"></param>
		/// <param name="e"></param>
		private void button1_Click(object sender, System.EventArgs e)
		{
			int i, j, level;
			complex_t p = new complex_t();
			complex_t a = new complex_t();
			complex_t []w = new complex_t[6];
			complex_t []d = new complex_t[5];

			Fractal.Image = new Bitmap(Fractal.Width, Fractal.Height);
			Graphics graph = Graphics.FromImage(Fractal.Image);
			graph.FillRectangle(new SolidBrush(Color.White), 0, 0, Fractal.Width, Fractal.Height);
			
			minX = double.Parse(minx.Text);
			minY = double.Parse(miny.Text);
			maxX = double.Parse(maxx.Text);
			maxY = double.Parse(maxy.Text);

			for (i=0; i<w.Length; i++)
			{
				w[i] = new complex_t();
			}
			for (i=0; i<d.Length; i++)
			{
				d[i] = new complex_t();
			}

			w[0].real = double.Parse(pr0.Text);
			w[0].imaginary = double.Parse(pi0.Text);
			w[1].real = double.Parse(pr1.Text);
			w[1].imaginary = double.Parse(pi1.Text);
			w[2].real = double.Parse(pr2.Text);
			w[2].imaginary = double.Parse(pi2.Text);
			w[3].real = double.Parse(pr3.Text);
			w[3].imaginary = double.Parse(pi3.Text);
			w[4].real = double.Parse(pr4.Text);
			w[4].imaginary = double.Parse(pi4.Text);
			w[5].real = double.Parse(pr5.Text);
			w[5].imaginary = double.Parse(pi5.Text);

			d[0].real = double.Parse(pr1.Text);
			d[0].imaginary = double.Parse(pi1.Text);
			d[1].real = 2.0*double.Parse(pr2.Text);
			d[1].imaginary = 2.0*double.Parse(pi2.Text);
			d[2].real = 3.0*double.Parse(pr3.Text);
			d[2].imaginary = 3.0*double.Parse(pi3.Text);
			d[3].real = 4.0*double.Parse(pr4.Text);
			d[3].imaginary = 4.0*double.Parse(pi4.Text);
			d[4].real = 5.0*double.Parse(pr5.Text);
			d[4].imaginary = 5.0*double.Parse(pi5.Text);

			a.real = double.Parse(aRe.Text);
			a.imaginary = double.Parse(aIm.Text);

			ratioX = (maxX - minX) / Fractal.Width;
			ratioY = (maxY - minY) / Fractal.Height;

			resultsCnt = 0;
			cSet = colorSet.Checked;

			for (i=0; i<Fractal.Height; i++)
			{
				p.imaginary = i*ratioY + minY;
				for (j=0; j<Fractal.Width; j++)
				{
					p.real = j*ratioX + minX;
					level = levelSet(a, p, w, d);
					graph.DrawRectangle(penColors[level-1], j, i, 1, 1);
				}
			}
			Fractal.Invalidate();	
		}

		//value is inside set in the returned level
		private int levelSet(complex_t a, complex_t p, complex_t [] w, complex_t [] d)
		{
			complex_t z = new complex_t();
			complex_t z_prev = new complex_t();
			int iteration;

			iteration = 0;
			z = p;

			do
			{
				z_prev = z;
				z = sub(z, mul(a, div(func(z, w), func(z, d))));
				iteration++;
			} while (sub(z_prev,z).complexModSq() > 0.0001 && iteration < 100);

			if (cSet == true)
			{
				if (iteration < 100)
				{
					return 10*findResult(z);
				}
			}

			return iteration;
		}

		//intialize form
		private void Form1_Load(object sender, System.EventArgs e)
		{
			minx.Text = ((double)-1.5).ToString();
			maxx.Text = ((double)1.5).ToString();
			miny.Text = ((double)-1.5).ToString();
			maxy.Text = ((double)1.5).ToString();

			aRe.Text = ((double)1.0).ToString();
			aIm.Text = ((double)0.0).ToString();

			pr0.Text = ((double)-1.0).ToString();
			pr1.Text = ((double)0.0).ToString();
			pr2.Text = ((double)0.0).ToString();
			pr3.Text = ((double)1.0).ToString();
			pr4.Text = ((double)0.0).ToString();
			pr5.Text = ((double)0.0).ToString();

			pi0.Text = ((double)0.0).ToString();
			pi1.Text = ((double)0.0).ToString();
			pi2.Text = ((double)0.0).ToString();
			pi3.Text = ((double)0.0).ToString();
			pi4.Text = ((double)0.0).ToString();
			pi5.Text = ((double)0.0).ToString();

			minX = double.Parse(minx.Text);
			minY = double.Parse(miny.Text);
			maxX = double.Parse(maxx.Text);
			maxY = double.Parse(maxy.Text);

			ratioX = (maxX - minX) / Fractal.Width;
			ratioY = (maxY - minY) / Fractal.Height;

			initializeColors();

			Fractal.Image = new Bitmap(Fractal.Width, Fractal.Height);
			graph = Graphics.FromImage(Fractal.Image);

			//render new fractal
			button1_Click(sender, e);
		}

		//draw selection
		private void Fractal_MouseDown(object sender, System.Windows.Forms.MouseEventArgs e)
		{
			if (e.Button == MouseButtons.Left)
			{
				downX = e.X;
				downY = e.Y;

				Selection.Width = 0;
				Selection.Height = 0;
				Selection.Visible = true;
			}
		}

		//redraw selection
		private void Fractal_MouseMove(object sender, System.Windows.Forms.MouseEventArgs e)
		{
			if (e.Button == MouseButtons.Left)
			{
				Selection.Width = Math.Abs(downX - e.X);
				Selection.Height = Math.Abs(downY - e.Y);
				Selection.Left = Fractal.Left + Math.Min(downX, e.X);
				Selection.Top = Fractal.Top + Math.Min(downY, e.Y);
			}
		}

		//clear selection - render new fractal for given selection
		private void Fractal_MouseUp(object sender, System.Windows.Forms.MouseEventArgs e)
		{
			//remove selection
			Selection.Visible = false;

			//get new range to render
			minx.Text = (Math.Min(downX, e.X)*ratioX + minX).ToString();
			maxx.Text = (Math.Max(downX, e.X)*ratioX + minX).ToString();
			miny.Text = (Math.Min(downY, e.Y)*ratioY + minY).ToString();
			maxy.Text = (Math.Max(downY, e.Y)*ratioY + minY).ToString();

			minX = double.Parse(minx.Text);
			minY = double.Parse(miny.Text);
			maxX = double.Parse(maxx.Text);
			maxY = double.Parse(maxy.Text);

			//render new fractal
			button1_Click(sender, e);		
		}
	}

	/// <summary>
	/// Class for complex numbers x = x.real + i*x.imaginary
	/// </summary>
	public class complex_t
	{
		public double real;
		public double imaginary;

		//calculate squared modus of given complex c
		public double complexModSq()
		{
			return (real*real + imaginary*imaginary);
		}
	}
}