/// <summary>
/// Divides this ComplexNum by a given one
/// </summary>
/// <param name="n">The ComplexNum to divide with</param>
public void Divide(ComplexNum n)
{
double a = real;
double b = complex;
double c = n.GetReal();
double d = n.GetComplex();
//Trust me on this one
real = (a * c + b * d) / (c * c + d * d);
complex = (b - a * d) / (c * c + d * d);
}
/// <summary>
/// Finds the product of a ComplexNum and this one
/// </summary>
/// <param name="n">The ComplexNum to be multiplied</param>
public void Multiply(ComplexNum n)
{
double a = real;
double b = complex;
double c = n.GetReal();
double d = n.GetComplex();
//Using FOIL to determine new values
//(a + bi)(c + di)
real = (a * c) - (b * d);
complex = (a * d) + (b * c);
}
/// <summary>
/// Recursive check if a complex number is within the Mandelbrot set
/// </summary>
/// <param name="z"></param>
/// <param name="c"></param>
/// <param name="recursions"></param>
/// <param name="maxRecursions"></param>
/// <returns>TRUE if "c" is within Mandelbrot Set, FALSE otherwise</returns>
private bool RecursiveCheck(ComplexNum z, ComplexNum c, int recursions, int maxRecursions)
{
if (Math.Sqrt(z.GetReal() * z.GetReal() + z.GetComplex() * z.GetComplex()) > MAX_DIST)
{
//Number blew up
return(false);
}
else if (recursions > maxRecursions)
{
//Number probably does not blow up
return(true);
}
else
{
//Run it again
z.Squared();
z.Add(c);
return(RecursiveCheck(z, c, recursions + 1, maxRecursions));
}
}
/// <summary>
/// Iterative check if a complex number is within the Mandelbrot set
/// </summary>
/// <param name="z"></param>
/// <param name="c"></param>
/// <param name="maxIterations"></param>
/// <returns>TRUE if "c" is within Mandelbrot Set, FALSE otherwise</returns>
private int IterativeCheck(ComplexNum z, ComplexNum c, int maxIterations)
{
int iterations = 0;
while (true)
{
if (z.Magnitude() > MAX_DIST)
{
//Number blew up
return(iterations);
}
else if (iterations >= maxIterations)
{
//Number probably does not blow up
return(maxIterations);
}
//Run it through the function again
z.Multiply(z);
z.Add(c);
iterations++;
}
}
/// <summary>
/// Generates set upon clicking button
/// </summary>
private void generateBtn_Click(object sender, EventArgs e)
{
//Objects used to draw the set
Graphics objGraphics = this.CreateGraphics();
Brush objBrush = new SolidBrush(System.Drawing.Color.Blue);
//Setting size of array based on size of window
domainSize = Math.Min(this.Size.Height, this.Size.Width);
//Parsing input for values, if it is valid
double.TryParse(topTxt.Text, out renderTop);
double.TryParse(leftTxt.Text, out renderLeft);
double.TryParse(sizeTxt.Text, out renderSideLength);
int.TryParse(bailOutTxt.Text, out bailOut);
//Showing values
topTxt.Text = renderTop.ToString();
leftTxt.Text = renderLeft.ToString();
sizeTxt.Text = renderSideLength.ToString();
bailOutTxt.Text = bailOut.ToString();
//Complex numbers
ComplexNum z = new ComplexNum(0, 0);
ComplexNum c = new ComplexNum(0, 0);
//Going through each point in the pointSet
for (int b = 0; b < domainSize; b++)
{
for (int a = 0; a < domainSize; a++)
{
//Setting complex value
c.SetReal(renderSideLength * ((double)a / (double)domainSize) + renderLeft);
c.SetComplex(renderSideLength * ((double)b / (double)domainSize) + renderTop);
z.SetReal(0);
z.SetComplex(0);
//Setting blow-up value for point
pointValue = IterativeCheck(z, c, bailOut);
if (pointValue == bailOut)
{
objBrush = new SolidBrush(System.Drawing.Color.Black);
}
else
{
//Setting brush shade
float s = (float)pointValue / (float)bailOut;
int t = (int)(Math.Log10(10 * s + 1) * 255);
if (t > 255)
{
t = 255;
}
int red = t;
int green = t;
int blue = 255 - t;
objBrush = new SolidBrush(System.Drawing.Color.FromArgb(red, green, blue));
}
//Drawing point
objGraphics.FillRectangle(objBrush, a, b, 1, 1);
}
//Ensures memory does not run out
GC.Collect();
GC.WaitForPendingFinalizers();
}
}
/// <summary>
/// Subtracts a ComplexNum value from this one
/// </summary>
/// <param name="n">The ComplexNum to be subtracted</param>
public void Subtract(ComplexNum n)
{
real -= n.GetReal();
complex -= n.GetComplex();
}
/// <summary>
/// Adds a ComplexNum value to this one
/// </summary>
/// <param name="n">The ComplexNum to be added</param>
public void Add(ComplexNum n)
{
real += n.GetReal();
complex += n.GetComplex();
}
