public static EscapeTime FindEscapeTimeNoCycleDetection(Complex c, int maxIterations)
{
if (MandelbulbChecker.IsInsideBulbs(c))
{
return(EscapeTime.Infinite);
}
var zReal = 0.0;
var zImag = 0.0;
var z2Real = 0.0;
var z2Imag = 0.0;
for (int i = 0; i < maxIterations; i++)
{
zImag = 2 * zReal * zImag + c.Imaginary;
zReal = z2Real - z2Imag + c.Real;
z2Real = zReal * zReal;
z2Imag = zImag * zImag;
if ((z2Real + z2Imag) > 4)
{
return(EscapeTime.Discrete(i));
}
}
return(EscapeTime.Infinite);
}
private Tuple <Point, Color> PickColorForPoint(Point point, Area viewPort, Size resolution, bool checkForEdges, IEnumerable <Area> areasToInclude)
{
var number = viewPort.GetNumberFromPoint(resolution, point);
var color = PickColor(
() => checkForEdges && areasToInclude.Any(a => a.IsInside(number)),
() => MandelbrotFinder.IsInSet(number),
() => MandelbulbChecker.IsInsideBulbs(number));
return(Tuple.Create(point, color));
}
public static bool IsInSet(Complex c, BailoutRange bailout)
{
if (MandelbulbChecker.IsInsideBulbs(c))
{
return(true);
}
double re = 0;
double im = 0;
// Check for orbits
// - Check re/im against an old point
// - Only check every power of 2
double oldRe = 0;
double oldIm = 0;
uint checkNum = 1;
// Cache the squares
// They are used to find the magnitude; reuse these values when computing the next re/im
double re2 = 0;
double im2 = 0;
for (uint i = 0; i < bailout.Maximum; i++)
{
var reTemp = re2 - im2 + c.Real;
im = 2 * re * im + c.Imaginary;
re = reTemp;
// Orbit check
if (checkNum == i)
{
if (IsPracticallyTheSame(oldRe, re) && IsPracticallyTheSame(oldIm, im))
{
return(true);
}
oldRe = re;
oldIm = im;
checkNum = checkNum << 1;
}
re2 = re * re;
im2 = im * im;
// Check the magnitude squared against 2^2
if ((re2 + im2) > 4)
{
return(false);
}
}
return(true);
}
/// <summary>
/// Determines whether the point is in the set, without using an arbitrary iteration limit.
/// </summary>
/// <param name="c">The c.</param>
/// <remarks>
/// Brent's Algorithm is used to detect cycles for points in the set.
/// </remarks>
/// <returns>
/// The <see cref="EscapeTime"/> of the point.
/// </returns>
public static EscapeTime FindEscapeTime(Complex c)
{
if (MandelbulbChecker.IsInsideBulbs(c))
{
return(EscapeTime.Infinite);
}
var zReal = 0.0f;
var zImag = 0.0f;
var z2Real = 0.0f;
var z2Imag = 0.0f;
var oldZReal = 0.0f;
var oldZImag = 0.0f;
var cReal = (float)c.Real;
var cImag = (float)c.Imaginary;
int stepsTaken = 0;
int stepLimit = 2;
int iterations = 0;
while ((z2Real + z2Imag) <= 4)
{
iterations++;
stepsTaken++;
zImag = 2 * zReal * zImag + cImag;
zReal = z2Real - z2Imag + cReal;
z2Real = zReal * zReal;
z2Imag = zImag * zImag;
if (oldZReal == zReal && oldZImag == zImag)
{
return(EscapeTime.Infinite);
}
if (stepsTaken == stepLimit)
{
oldZReal = zReal;
oldZImag = zImag;
stepsTaken = 0;
stepLimit = stepLimit << 1;
}
}
return(EscapeTime.Discrete(iterations));
}
public static EscapeTime FindEscapeTime(Complex c, int maxIterations)
{
if (MandelbulbChecker.IsInsideBulbs(c))
{
return(EscapeTime.Infinite);
}
var zReal = 0.0f;
var zImag = 0.0f;
var z2Real = 0.0f;
var z2Imag = 0.0f;
var oldZReal = 0.0f;
var oldZImag = 0.0f;
int stepsTaken = 0;
int stepLimit = 2;
for (int i = 0; i < maxIterations; i++)
{
stepsTaken++;
zImag = 2 * zReal * zImag + (float)c.Imaginary;
zReal = z2Real - z2Imag + (float)c.Real;
if (oldZReal == zReal && oldZImag == zImag)
{
return(EscapeTime.Infinite);
}
z2Real = zReal * zReal;
z2Imag = zImag * zImag;
if ((z2Real + z2Imag) > 4)
{
return(EscapeTime.Discrete(i));
}
if (stepsTaken == stepLimit)
{
oldZReal = zReal;
oldZImag = zImag;
stepsTaken = 0;
stepLimit = stepLimit << 1;
}
}
return(EscapeTime.Infinite);
}
public static double FindDistance(Complex c, int maxIterations)
{
if (MandelbulbChecker.IsInsideBulbs(c))
{
return(0);
}
var z = Complex.Zero;
var oldZ = Complex.Zero;
var dZ = Complex.Zero;
int stepsTaken = 0;
int stepLimit = 2;
for (int i = 0; i < maxIterations; i++)
{
stepsTaken++;
dZ = 2 * z * dZ + 1;
z = z * z + c;
if (oldZ == z)
{
return(0);
}
if (z.MagnitudeSquared() > 4)
{
break;
}
if (stepsTaken == stepLimit)
{
oldZ = z;
stepsTaken = 0;
stepLimit = stepLimit << 1;
}
}
var magZ = z.Magnitude;
var magDZ = dZ.Magnitude;
return(2 * Math.Log(magZ * magZ) * magZ / magDZ);
}
protected override bool ValidatePoint(Complex point)
{
return(!MandelbulbChecker.IsInsideBulbs(point));
}
