public static FractalGraph CalcNovaJulia(double rCenter, double iCenter, double R0, double I0,
double rDelta, double Rr, double Ri, double pr, double pi, SKColor[] Palette,
int Width, int Height, ScriptNode Node, Variables Variables,
FractalZoomScript FractalZoomScript, object State)
{
double r0, i0, r1, i1;
double dr, di;
double r, i;
double zr, zi, zr2, zi2, zr3, zi3, zr4, zi4;
double aspect;
double Temp;
int x, y;
int n, N;
int index;
double lnz;
double argz;
double amp;
double phi;
N = Palette.Length;
int Size = Width * Height;
double[] ColorIndex = new double[Size];
double Conv = 1e-10;
double Div = 1e10;
rDelta *= 0.5;
r0 = rCenter - rDelta;
r1 = rCenter + rDelta;
aspect = ((double)Width) / Height;
i0 = iCenter - rDelta / aspect;
i1 = iCenter + rDelta / aspect;
dr = (r1 - r0) / Width;
di = (i1 - i0) / Height;
for (y = 0, i = i0, index = 0; y < Height; y++, i += di)
{
for (x = 0, r = r0; x < Width; x++, r += dr)
{
zr = r;
zi = i;
n = 0;
do
{
// f: z->z^p-1 = exp(p*ln(z))-1
// exp(a+ib)=exp(a)*(cos(b)+i*sin(b))
// ln(z)=ln|z|+i*arg(z)
// exp(p*ln(z))-1 =
// = exp((pr+i*pi)*(ln|z|+i*arg(z)))-1 =
// = exp(pr*ln|z|-pi*arg(z)+i*(pi*ln|z|+pr*arg(z)))-1 =
// = exp(pr*ln|z|-pi*arg(z))*(cos(pi*ln|z|+pr*arg(z))+i*sin(pi*ln|z|+pr*arg(z)))-1
lnz = System.Math.Log(Math.Sqrt(zr * zr + zi * zi));
argz = System.Math.Atan2(zi, zr);
amp = System.Math.Exp(pr * lnz - pi * argz);
phi = pi * lnz + pr * argz;
zr2 = amp * System.Math.Cos(phi) - 1;
zi2 = amp * System.Math.Sin(phi);
// f': z->p*z^(p-1) = p*exp((p-1)*ln(z)) =
// = (pr+i*pi)*exp((pr-1+i*pi)*(ln|z|+i*arg(z))) =
// = (pr+i*pi)*exp((pr-1)*ln|z|-pi*arg(z)+i*(pi*ln|z|+(pr-1)*arg(z))) =
// = (pr+i*pi)*exp((pr-1)*ln|z|-pi*arg(z))(sin(pi*ln|z|+(pr-1)*arg(z))+i*cos(pi*ln|z|+(pr-1)*arg(z))) =
amp = System.Math.Exp((pr - 1) * lnz - pi * argz);
phi = pi * lnz + (pr - 1) * argz;
zr3 = amp * System.Math.Cos(phi);
zi3 = amp * System.Math.Sin(phi);
Temp = pr * zr3 - pi * zi3;
zi3 = pr * zi3 + pi * zr3;
zr3 = Temp;
// f/f':
Temp = 1.0 / (zr3 * zr3 + zi3 * zi3);
zr4 = (zr2 * zr3 + zi2 * zi3) * Temp;
zi4 = (zi2 * zr3 - zr2 * zi3) * Temp;
Temp = Rr * zr4 - Ri * zi4;
zi4 = Ri * zr4 + Rr * zi4 + I0;
zr4 = Temp + R0;
zr -= zr4;
zi -= zi4;
Temp = Math.Sqrt(zr4 * zr4 + zi4 * zi4);
}while ((Temp > Conv) && (Temp < Div) && (n++ < N));
if (Temp < Conv && n < N)
{
ColorIndex[index++] = n;
}
else
{
ColorIndex[index++] = N;
}
}
}
Node.Expression.Preview(new GraphBitmap(FractalGraph.ToBitmap(ColorIndex, Width, Height, Palette)));
double[] Boundary = FractalGraph.FindBoundaries(ColorIndex, Width, Height);
FractalGraph.Smooth(ColorIndex, Boundary, Width, Height, N, Palette, Node, Variables);
return(new FractalGraph(FractalGraph.ToBitmap(ColorIndex, Width, Height, Palette),
r0, i0, r1, i1, rDelta * 2, true, Node, FractalZoomScript, State));
}
public static FractalGraph CalcNewtonSmooth(double rCenter, double iCenter, double rDelta, Complex R,
ILambdaExpression f, ScriptNode fDef, Variables Variables, SKColor[] Palette, int Width, int Height,
ScriptNode Node, FractalZoomScript FractalZoomScript, object State)
{
double RRe = R.Real;
double RIm = R.Imaginary;
double r0, i0, r1, i1;
double dr, di;
double r, i;
double aspect;
int x, y;
int n, N;
N = Palette.Length;
if (Width <= 2 || Height <= 2)
{
throw new ScriptRuntimeException("Width and Height has to be greater than 2.", Node);
}
Variables v = new Variables();
Variables.CopyTo(v);
if (!(f is IDifferentiable Differentiable) ||
!(Differentiable.Differentiate(Differentiable.DefaultVariableName, v) is ILambdaExpression fPrim))
{
throw new ScriptRuntimeException("Lambda expression not differentiable.", Node);
}
int Size = Width * Height;
double Conv = 1e-10;
double Div = 1e10;
double[] ColorIndex = new double[Size];
int Index = 0;
Complex[] Row;
Complex[] Row2;
Complex[] Row3;
int[] Offset;
IElement[] P = new IElement[1];
int j, c, x2;
IElement Obj, Obj2;
double Mod;
Complex z;
rDelta *= 0.5;
r0 = rCenter - rDelta;
r1 = rCenter + rDelta;
aspect = ((double)Width) / Height;
i0 = iCenter - rDelta / aspect;
i1 = iCenter + rDelta / aspect;
dr = (r1 - r0) / Width;
di = (i1 - i0) / Height;
for (y = 0, i = i0; y < Height; y++, i += di)
{
Row = new Complex[Width];
Offset = new int[Width];
c = Width;
for (x = 0, x2 = y * Width, r = r0; x < Width; x++, r += dr, x2++)
{
Row[x] = new Complex(r, i);
Offset[x] = x2;
}
n = 0;
while (n < N && c > 0)
{
n++;
P[0] = Expression.Encapsulate(Row);
Obj = f.Evaluate(P, v);
Obj2 = fPrim.Evaluate(P, v);
Row2 = Obj.AssociatedObjectValue as Complex[];
Row3 = Obj2.AssociatedObjectValue as Complex[];
if (Row2 == null || Row3 == null)
{
throw new ScriptRuntimeException("Lambda expression (and its first derivative) must be able to accept complex vectors, " +
"and return complex vectors of equal length. Type returned: " +
Obj.GetType().FullName + " and " + Obj2.GetType().FullName, Node);
}
else if (Row2.Length != c || Row3.Length != c)
{
throw new ScriptRuntimeException("Lambda expression (and its first derivative) must be able to accept complex vectors, " +
"and return complex vectors of equal length. Length returned: " +
Row2.Length.ToString() + " and " + Row3.Length.ToString() +
". Expected: " + c.ToString(), Node);
}
for (x = x2 = 0; x < c; x++)
{
j = Offset[x];
z = R * Row2[x] / Row3[x];
Row[x] -= z;
Mod = z.Magnitude;
if (Mod > Conv && Mod < Div)
{
if (x != x2)
{
Offset[x2] = j;
}
x2++;
}
else
{
if (n >= N)
{
ColorIndex[Index++] = N;
}
else
{
ColorIndex[j++] = n;
}
}
}
if (x2 < x)
{
Array.Resize <Complex>(ref Row, x2);
Array.Resize <int>(ref Offset, x2);
c = x2;
}
}
}
Node.Expression.Preview(new GraphBitmap(FractalGraph.ToBitmap(ColorIndex, Width, Height, Palette)));
double[] Boundary = FractalGraph.FindBoundaries(ColorIndex, Width, Height);
FractalGraph.Smooth(ColorIndex, Boundary, Width, Height, N, Palette, Node, Variables);
return(new FractalGraph(FractalGraph.ToBitmap(ColorIndex, Width, Height, Palette),
r0, i0, r1, i1, rDelta * 2, true, Node, FractalZoomScript, State));
}
public static FractalGraph CalcNewtonSmooth(double rCenter, double iCenter, double rDelta, Complex R,
Complex[] Coefficients, SKColor[] Palette, int Width, int Height, ScriptNode Node, Variables Variables,
FractalZoomScript FractalZoomScript, object State)
{
double RRe = R.Real;
double RIm = R.Imaginary;
double r0, i0, r1, i1;
double dr, di;
double r, i;
double zr, zi, zr2, zi2, zr3, zi3, zr4, zi4;
double aspect;
double Temp;
int x, y;
int n, N;
int Degree = Coefficients.Length - 1;
N = Palette.Length;
if (Degree < 2)
{
Array.Resize <Complex>(ref Coefficients, 3);
while (Degree < 2)
{
Coefficients[++Degree] = Complex.Zero;
}
}
if (Width <= 2 || Height <= 2)
{
throw new ScriptRuntimeException("Width and Height has to be greater than 2.", Node);
}
Complex[] Prim = new Complex[Degree];
for (x = 1; x <= Degree; x++)
{
Prim[x - 1] = x * Coefficients[x];
}
Array.Reverse(Prim);
Coefficients = (Complex[])Coefficients.Clone();
Array.Reverse(Coefficients);
int j, c = Prim.Length;
double[] ReC = new double[c + 1];
double[] ImC = new double[c + 1];
double[] RePrim = new double[c];
double[] ImPrim = new double[c];
Complex z;
for (j = 0; j < c; j++)
{
z = Coefficients[j];
ReC[j] = z.Real;
ImC[j] = z.Imaginary;
z = Prim[j];
RePrim[j] = z.Real;
ImPrim[j] = z.Imaginary;
}
z = Coefficients[j];
ReC[j] = z.Real;
ImC[j] = z.Imaginary;
int Size = Width * Height;
double Conv = 1e-10;
double Div = 1e10;
double[] ColorIndex = new double[Size];
int Index = 0;
rDelta *= 0.5;
r0 = rCenter - rDelta;
r1 = rCenter + rDelta;
aspect = ((double)Width) / Height;
i0 = iCenter - rDelta / aspect;
i1 = iCenter + rDelta / aspect;
dr = (r1 - r0) / Width;
di = (i1 - i0) / Height;
for (y = 0, i = i0; y < Height; y++, i += di)
{
for (x = 0, r = r0; x < Width; x++, r += dr)
{
zr = r;
zi = i;
n = 0;
do
{
// f:
zr2 = zi2 = 0;
for (j = 0; j <= c; j++)
{
Temp = zr2 * zr - zi2 * zi + ReC[j];
zi2 = zr2 * zi + zi2 * zr + ImC[j];
zr2 = Temp;
}
// f':
zr3 = zi3 = 0;
for (j = 0; j < c; j++)
{
Temp = zr3 * zr - zi3 * zi + RePrim[j];
zi3 = zr3 * zi + zi3 * zr + ImPrim[j];
zr3 = Temp;
}
// f/f':
Temp = 1.0 / (zr3 * zr3 + zi3 * zi3);
zr4 = (zr2 * zr3 + zi2 * zi3) * Temp;
zi4 = (zi2 * zr3 - zr2 * zi3) * Temp;
// R*f/f'
Temp = zr4 * RRe - zi4 * RIm;
zi4 = zr4 * RIm + zi4 * RRe;
zr4 = Temp;
zr -= zr4;
zi -= zi4;
Temp = Math.Sqrt(zr4 * zr4 + zi4 * zi4);
}while ((Temp > Conv) && (Temp < Div) && (n++ < N));
if (Temp < Conv && n < N)
{
ColorIndex[Index++] = n;
}
else
{
ColorIndex[Index++] = N;
}
}
}
Node.Expression.Preview(new GraphBitmap(FractalGraph.ToBitmap(ColorIndex, Width, Height, Palette)));
double[] Boundary = FractalGraph.FindBoundaries(ColorIndex, Width, Height);
FractalGraph.Smooth(ColorIndex, Boundary, Width, Height, N, Palette, Node, Variables);
return(new FractalGraph(FractalGraph.ToBitmap(ColorIndex, Width, Height, Palette),
r0, i0, r1, i1, rDelta * 2, true, Node, FractalZoomScript, State));
}
public static FractalGraph CalcJulia(double rCenter, double iCenter, ILambdaExpression f,
ScriptNode fDef, double rDelta, SKColor[] Palette, int Width, int Height, ScriptNode Node,
Variables Variables, FractalZoomScript FractalZoomScript, object State)
{
double r0, i0, r1, i1;
double dr, di;
double r, i;
double aspect;
int x, y;
int n, N;
N = Palette.Length;
rDelta *= 0.5;
r0 = rCenter - rDelta;
r1 = rCenter + rDelta;
aspect = ((double)Width) / Height;
i0 = iCenter - rDelta / aspect;
i1 = iCenter + rDelta / aspect;
dr = (r1 - r0) / Width;
di = (i1 - i0) / Height;
int Size = Width * Height;
double[] ColorIndex = new double[Size];
int c, j, x2;
Complex z;
IElement[] P = new IElement[1];
IElement Obj;
double Mod;
for (y = 0, i = i0; y < Height; y++, i += di)
{
Complex[] Row = new Complex[Width];
int[] Offset = new int[Width];
c = Width;
for (x = 0, x2 = y * Width, r = r0; x < Width; x++, r += dr, x2++)
{
Row[x] = new Complex(r, i);
Offset[x] = x2;
}
n = 0;
while (n < N && c > 0)
{
n++;
P[0] = Expression.Encapsulate(Row);
Obj = f.Evaluate(P, Variables);
Row = Obj.AssociatedObjectValue as Complex[];
if (Row == null)
{
throw new ScriptRuntimeException("Lambda expression must be able to accept complex vectors, " +
"and return complex vectors of equal length. Type returned: " +
Obj.GetType().FullName, Node);
}
else if (Row.Length != c)
{
throw new ScriptRuntimeException("Lambda expression must be able to accept complex vectors, " +
"and return complex vectors of equal length. Length returned: " +
Row.Length.ToString() + ". Expected: " + c.ToString(), Node);
}
for (x = x2 = 0; x < c; x++)
{
z = Row[x];
j = Offset[x];
Mod = z.Magnitude;
if (Mod < 3)
{
if (x != x2)
{
Row[x2] = z;
Offset[x2] = j;
}
x2++;
}
else
{
ColorIndex[j++] = n;
}
}
if (x2 < x)
{
Array.Resize <Complex>(ref Row, x2);
Array.Resize <int>(ref Offset, x2);
c = x2;
}
}
if (c > 0)
{
for (x = 0; x < c; x++)
{
j = Offset[x];
ColorIndex[j] = N;
}
}
}
Node.Expression.Preview(new GraphBitmap(FractalGraph.ToBitmap(ColorIndex, Width, Height, Palette)));
double[] Boundary = FractalGraph.FindBoundaries(ColorIndex, Width, Height);
FractalGraph.Smooth(ColorIndex, Boundary, Width, Height, N, Palette, Node, Variables);
return(new FractalGraph(FractalGraph.ToBitmap(ColorIndex, Width, Height, Palette),
r0, i0, r1, i1, rDelta * 2, true, Node, FractalZoomScript, State));
}
public static FractalGraph CalcJulia(double rCenter, double iCenter, double R0, double I0, double rDelta,
SKColor[] Palette, int Width, int Height, ScriptNode Node, Variables Variables,
FractalZoomScript FractalZoomScript, object State)
{
double r0, i0, r1, i1;
double dr, di;
double r, i;
double zr, zi, zrt, zr2, zi2;
double aspect;
int x, y;
int n, N;
int index;
N = Palette.Length;
rDelta *= 0.5;
r0 = rCenter - rDelta;
r1 = rCenter + rDelta;
aspect = ((double)Width) / Height;
i0 = iCenter - rDelta / aspect;
i1 = iCenter + rDelta / aspect;
dr = (r1 - r0) / Width;
di = (i1 - i0) / Height;
int Size = Width * Height;
double[] ColorIndex = new double[Size];
for (y = 0, i = i0, index = 0; y < Height; y++, i += di)
{
for (x = 0, r = r0; x < Width; x++, r += dr)
{
zr = r;
zi = i;
n = 0;
zr2 = zr * zr;
zi2 = zi * zi;
while (zr2 + zi2 < 9 && n < N)
{
n++;
zrt = zr2 - zi2 + R0;
zi = 2 * zr * zi + I0;
zr = zrt;
zr2 = zr * zr;
zi2 = zi * zi;
}
if (n >= N)
{
ColorIndex[index++] = N;
}
else
{
ColorIndex[index++] = n;
}
}
}
Node.Expression.Preview(new GraphBitmap(FractalGraph.ToBitmap(ColorIndex, Width, Height, Palette)));
double[] Boundary = FractalGraph.FindBoundaries(ColorIndex, Width, Height);
FractalGraph.Smooth(ColorIndex, Boundary, Width, Height, N, Palette, Node, Variables);
return(new FractalGraph(FractalGraph.ToBitmap(ColorIndex, Width, Height, Palette),
r0, i0, r1, i1, rDelta * 2, true, Node, FractalZoomScript, State));
}
public static FractalGraph CalcHalley(double rCenter, double iCenter, double rDelta, Complex R,
Complex[] Coefficients, SKColor[] Palette, int Width, int Height, ScriptNode Node, Variables Variables,
FractalZoomScript FractalZoomScript, object State)
{
double RRe = R.Real;
double RIm = R.Imaginary;
double r0, i0, r1, i1;
double dr, di;
double r, i;
double zr, zi, zr2, zi2, zr3, zi3, zr4, zi4, zr5, zi5, zr6, zi6;
double aspect;
double Temp;
int x, y;
int n, N;
int index;
int Degree = Coefficients.Length - 1;
N = Palette.Length;
if (Degree < 3)
{
Array.Resize <Complex>(ref Coefficients, 4);
while (Degree < 3)
{
Coefficients[++Degree] = Complex.Zero;
}
}
Complex[] Prim = new Complex[Degree];
for (x = 1; x <= Degree; x++)
{
Prim[x - 1] = x * Coefficients[x];
}
Complex[] Bis = new Complex[Degree - 1];
for (x = 1; x < Degree; x++)
{
Bis[x - 1] = x * Prim[x];
}
Array.Reverse(Bis);
Array.Reverse(Prim);
Coefficients = (Complex[])Coefficients.Clone();
Array.Reverse(Coefficients);
int j, c = Prim.Length;
int c2 = c - 1;
double[] ReC = new double[c + 1];
double[] ImC = new double[c + 1];
double[] RePrim = new double[c];
double[] ImPrim = new double[c];
double[] ReBis = new double[c2];
double[] ImBis = new double[c2];
Complex z;
for (j = 0; j < c; j++)
{
z = Coefficients[j];
ReC[j] = z.Real;
ImC[j] = z.Imaginary;
z = Prim[j];
RePrim[j] = z.Real;
ImPrim[j] = z.Imaginary;
if (j < c2)
{
z = Bis[j];
ReBis[j] = z.Real;
ImBis[j] = z.Imaginary;
}
}
z = Coefficients[j];
ReC[j] = z.Real;
ImC[j] = z.Imaginary;
int size = Width * Height;
double[] ColorIndex = new double[size];
double Conv = 1e-10;
double Div = 1e10;
rDelta *= 0.5;
r0 = rCenter - rDelta;
r1 = rCenter + rDelta;
aspect = ((double)Width) / Height;
i0 = iCenter - rDelta / aspect;
i1 = iCenter + rDelta / aspect;
dr = (r1 - r0) / Width;
di = (i1 - i0) / Height;
for (y = 0, i = i0, index = 0; y < Height; y++, i += di)
{
for (x = 0, r = r0; x < Width; x++, r += dr)
{
zr = r;
zi = i;
n = 0;
do
{
// f:
zr2 = zi2 = 0;
for (j = 0; j <= c; j++)
{
Temp = zr2 * zr - zi2 * zi + ReC[j];
zi2 = zr2 * zi + zi2 * zr + ImC[j];
zr2 = Temp;
}
// f':
zr3 = zi3 = 0;
for (j = 0; j < c; j++)
{
Temp = zr3 * zr - zi3 * zi + RePrim[j];
zi3 = zr3 * zi + zi3 * zr + ImPrim[j];
zr3 = Temp;
}
// f":
zr4 = zi4 = 0;
for (j = 0; j < c2; j++)
{
Temp = zr4 * zr - zi4 * zi + ReBis[j];
zi4 = zr4 * zi + zi4 * zr + ImBis[j];
zr4 = Temp;
}
// 2*f*f'
zr5 = 2 * (zr2 * zr3 - zi2 * zi3);
zi5 = 2 * (zr2 * zi3 + zi2 * zr3);
// 2f'^2-f*f"
zr6 = 2 * (zr3 * zr3 - zi3 * zi3) - (zr2 * zr4 - zi2 * zi4);
zi6 = 4 * zr3 * zi3 - (zr2 * zi4 + zr4 * zi2);
// R*2*f*f'/2f'^2-f*f"
Temp = 1.0 / (zr6 * zr6 + zi6 * zi6);
zr4 = (zr5 * zr6 + zi5 * zi6) * Temp;
zi4 = (zi5 * zr6 - zr5 * zi6) * Temp;
// R*2*f*f'/(2f'^2-f*f")
Temp = zr4 * RRe - zi4 * RIm;
zi4 = zr4 * RIm + zi4 * RRe;
zr4 = Temp;
zr -= zr4;
zi -= zi4;
Temp = Math.Sqrt(zr4 * zr4 + zi4 * zi4);
}while ((Temp > Conv) && (Temp < Div) && (n++ < N));
if (Temp < Conv && n < N)
{
ColorIndex[index++] = n;
}
else
{
ColorIndex[index++] = N;
}
}
}
Node.Expression.Preview(new GraphBitmap(FractalGraph.ToBitmap(ColorIndex, Width, Height, Palette)));
double[] Boundary = FractalGraph.FindBoundaries(ColorIndex, Width, Height);
FractalGraph.Smooth(ColorIndex, Boundary, Width, Height, N, Palette, Node, Variables);
return(new FractalGraph(FractalGraph.ToBitmap(ColorIndex, Width, Height, Palette),
r0, i0, r1, i1, rDelta * 2, true, Node, FractalZoomScript, State));
}
