public ComplexNumber ComplexFunctionDerivativeValue(ComplexNumber z0In)
{
ComplexNumber z = null;
z = ComplexOperations.Multiply(z0In, 2.0);
return(z);
}
// used in Mandelbrot set fractal
public ComplexNumber ComplexFunctionValue(ComplexNumber z0In)
{
ComplexNumber z = null;
z = ComplexOperations.Multiply(z0In, z0In);
return(z);
}
public ComputedFractalValues ReturnComputedFractalValues(RectangleInPlane fractalRectangleIn, int xMaxIn, int yMaxIn, IList <FractalColorValue> fractalColorValuesIn, System.Windows.Forms.ProgressBar fractalProgressIn)
{
if (fractalColorValuesIn.Count < NumberOfColorUsed)
{
throw new FractalObserverException("Fractal PythagorasTree needs more colors that are available in the input parameter fractalColorValuesIn!");
}
ComputedFractalValues aComputedFractalValuesValues = new ComputedFractalValues();
for (int aCurrentYPos = 0; aCurrentYPos < yMaxIn; aCurrentYPos++)
{
fractalProgressIn.Value = (int)(100.0 * ((double)aCurrentYPos / (double)yMaxIn));
for (int aCurrentXPos = 0; aCurrentXPos < xMaxIn; aCurrentXPos++)
{
int tempValue = 0;
ComplexNumber c = new ComplexNumber();
c.Re = fractalRectangleIn.StartX + Math.Abs(fractalRectangleIn.StartX - fractalRectangleIn.EndX) * ((double)aCurrentXPos / (double)xMaxIn);
c.Im = fractalRectangleIn.StartY + Math.Abs(fractalRectangleIn.StartY - fractalRectangleIn.EndY) * ((double)aCurrentYPos / (double)yMaxIn);
int n = 0;
myZValues[n].Re = 0.0;
myZValues[n].Im = 0.0;
// computation of value for function z2+c, if it converges (if it is bounded) the point is part of mandelbrot set
do
{
n++;
myZValues[n] = ComplexOperations.Add(Equation.ComplexFunctionValue(myZValues[n - 1]), c);
} while (((Math.Abs(myZValues[n].Re) < myMaximumValueForConvergation) && (Math.Abs(myZValues[n].Im) < myMaximumValueForConvergation)) && (n < (MaximumNumberOfIterations - 1)));
tempValue = n;
ComputedFractalValue aCFValue = new ComputedFractalValue();
FractalColorValue aFractalColorValue = ReturnColor(tempValue, fractalColorValuesIn);
aCFValue.ColorValue = aFractalColorValue;
aCFValue.AddComputedPoint(new System.Drawing.Point(aCurrentXPos, aCurrentYPos));
aCFValue.TypeOfShape = TypesOfShape.Point;
aCFValue.UsedTypeOfCoordinateSystem = TypesOfCoordinateSystem.Screen;
aComputedFractalValuesValues.AddComputedFractalValue(aCFValue);
}
}
return(aComputedFractalValuesValues);
}
public ComplexNumber ComplexFunctionValue(ComplexNumber z0In)
{
ComplexNumber z = null;
z = ComplexOperations.Multiply(z0In, z0In);
z = ComplexOperations.Multiply(z, z0In);
ComplexNumber tempZ = ComplexOperations.Multiply(z0In, 2.0);
z = ComplexOperations.Substract(z, tempZ);
z.Re += 2.0;
return(z);
}
public ComputedFractalValues ReturnComputedFractalValues(RectangleInPlane fractalRectangleIn, int xMaxIn, int yMaxIn, IList <FractalColorValue> fractalColorValuesIn, System.Windows.Forms.ProgressBar fractalProgressIn)
{
if (fractalColorValuesIn.Count < NumberOfColorUsed)
{
throw new FractalObserverException("Fractal PythagorasTree needs more colors that are available in the input parameter fractalColorValuesIn!");
}
ComputedFractalValues aComputedFractalValues = new ComputedFractalValues();
myZRoots.Clear();
for (int aCurrentYPos = 0; aCurrentYPos < yMaxIn; aCurrentYPos++)
{
fractalProgressIn.Value = (int)(100.0 * ((double)aCurrentYPos / (double)yMaxIn));
for (int aCurrentXPos = 0; aCurrentXPos < xMaxIn; aCurrentXPos++)
{
int tempRoot = 0;
int tempValue = 0;
int n = 0;
// initial values
myZValues[n].Re = fractalRectangleIn.StartX + Math.Abs(fractalRectangleIn.StartX - fractalRectangleIn.EndX) * ((double)aCurrentXPos / (double)xMaxIn);
myZValues[n].Im = fractalRectangleIn.StartY + Math.Abs(fractalRectangleIn.StartY - fractalRectangleIn.EndY) * ((double)aCurrentYPos / (double)yMaxIn);
// computation of next values until the maximum iteration count or until the conditions are met
do
{
n++;
myZValues[n] = ComplexOperations.Substract(myZValues[n - 1], ComplexOperations.Divide(Equation.ComplexFunctionValue(myZValues[n - 1]), Equation.ComplexFunctionDerivativeValue(myZValues[n - 1])));
} while (((Math.Abs(myZValues[n].Re - myZValues[n - 1].Re) > myTreshold) || (Math.Abs(myZValues[n].Im - myZValues[n - 1].Im) > myTreshold)) && (n < (MaximumNumberOfIterations - 1)));
ComputedFractalValue aCFValue = null;
FractalColorValue aFractalColorValue;
// if the solution did not converge to root, then return zero values
if (n >= (MaximumNumberOfIterations - 1) || double.IsNaN(myZValues[n].Re) || double.IsNaN(myZValues[n].Im))
{
aCFValue = new ComputedFractalValue();
aFractalColorValue = ReturnColor(tempRoot, tempValue, fractalColorValuesIn);
aCFValue.ColorValue = aFractalColorValue;
aCFValue.AddComputedPoint(new System.Drawing.Point(aCurrentXPos, aCurrentYPos));
aCFValue.TypeOfShape = TypesOfShape.Point;
aCFValue.UsedTypeOfCoordinateSystem = TypesOfCoordinateSystem.Screen;
aComputedFractalValues.AddComputedFractalValue(aCFValue);
continue;
}
bool aNewRoot = true;
int aRootNumber = 0;
// find out if the root is new until now, or if the current root was found already
for (int i = 0; i < myZRoots.Count; i++)
{
if ((Math.Abs(myZRoots[i].Re - myZValues[n].Re) < myTreshold) && (Math.Abs(myZRoots[i].Im - myZValues[n].Im) < myTreshold))
{
aNewRoot = false;
aRootNumber = i;
break;
}
}
// if this root is new until now, add new item to myZRoots List
if (aNewRoot)
{
ComplexNumber aComplexRoot = new ComplexNumber();
aComplexRoot.Re = myZValues[n].Re;
aComplexRoot.Im = myZValues[n].Im;
myZRoots.Add(aComplexRoot);
aRootNumber = myZRoots.Count - 1;
}
// sets the computed values for this pixel to return structure and return it
tempValue = n;
if (aRootNumber == 0)
{
tempRoot = 1;
}
else if (aRootNumber == 1)
{
tempRoot = 2;
}
else if (aRootNumber == 2)
{
tempRoot = 3;
}
else
{
throw new FractalObserverException("Error occured during computation of fractal, wrong number of roots was found!");
}
// storing of output of computation
aCFValue = new ComputedFractalValue();
aFractalColorValue = ReturnColor(tempRoot, tempValue, fractalColorValuesIn);
aCFValue.ColorValue = aFractalColorValue;
aCFValue.AddComputedPoint(new System.Drawing.Point(aCurrentXPos, aCurrentYPos));
aCFValue.TypeOfShape = TypesOfShape.Point;
aCFValue.UsedTypeOfCoordinateSystem = TypesOfCoordinateSystem.Screen;
aComputedFractalValues.AddComputedFractalValue(aCFValue);
}
}
return(aComputedFractalValues);
}