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HalleyTopographyFractal.cs
1using System;
2using System.Numerics;
3using System.Text;
4using SkiaSharp;
5using Waher.Script.Abstraction.Elements;
6using Waher.Script.Model;
7using Waher.Script.Exceptions;
8using Waher.Script.Objects.VectorSpaces;
9
10namespace Waher.Script.Fractals.ComplexFractals
11{
39 public class HalleyTopographyFractal : FunctionMultiVariate
40 {
44 public HalleyTopographyFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode Coefficients,
45 ScriptNode Palette, ScriptNode DimX, ScriptNode DimY, int Start, int Length, Expression Expression)
46 : base(new ScriptNode[] { z, dr, R, Coefficients, Palette, DimX, DimY },
47 new ArgumentType[] { ArgumentType.Scalar, ArgumentType.Scalar, ArgumentType.Scalar,
48 ArgumentType.Normal, ArgumentType.Vector, ArgumentType.Scalar, ArgumentType.Scalar}, Start, Length, Expression)
49 {
50 }
51
55 public HalleyTopographyFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode Coefficients,
56 ScriptNode Palette, ScriptNode DimX, int Start, int Length, Expression Expression)
57 : base(new ScriptNode[] { z, dr, R, Coefficients, Palette, DimX },
58 new ArgumentType[] { ArgumentType.Scalar, ArgumentType.Scalar, ArgumentType.Scalar,
59 ArgumentType.Normal, ArgumentType.Vector, ArgumentType.Scalar}, Start, Length, Expression)
60 {
61 }
62
66 public HalleyTopographyFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode Coefficients,
67 ScriptNode Palette, int Start, int Length, Expression Expression)
68 : base(new ScriptNode[] { z, dr, R, Coefficients, Palette },
69 new ArgumentType[] { ArgumentType.Scalar, ArgumentType.Scalar, ArgumentType.Scalar,
70 ArgumentType.Normal, ArgumentType.Vector}, Start, Length, Expression)
71 {
72 }
73
77 public HalleyTopographyFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode Coefficients,
78 int Start, int Length, Expression Expression)
79 : base(new ScriptNode[] { z, dr, R, Coefficients },
80 new ArgumentType[] { ArgumentType.Scalar, ArgumentType.Scalar, ArgumentType.Scalar,
81 ArgumentType.Normal}, Start, Length, Expression)
82 {
83 }
84
88 public HalleyTopographyFractal(ScriptNode z, ScriptNode dr, ScriptNode R, int Start, int Length, Expression Expression)
89 : base(new ScriptNode[] { z, dr, R },
90 new ArgumentType[] { ArgumentType.Scalar, ArgumentType.Scalar, ArgumentType.Scalar }, Start, Length, Expression)
91 {
92 }
93
97 public HalleyTopographyFractal(ScriptNode z, ScriptNode dr, int Start, int Length, Expression Expression)
98 : base(new ScriptNode[] { z, dr },
99 new ArgumentType[] { ArgumentType.Scalar, ArgumentType.Scalar }, Start, Length, Expression)
100 {
101 }
102
106 public override string[] DefaultArgumentNames
107 {
108 get
109 {
110 return new string[] { "z", "dr", "R", "Coefficients", "Palette", "DimX", "DimY" };
111 }
112 }
113
117 public override IElement Evaluate(IElement[] Arguments, Variables Variables)
118 {
119 string ColorExpression = null;
120 SKColor[] Palette;
121 double[] Coefficients = null;
122 Complex[] CoefficientsZ = null;
123 ILambdaExpression f = null;
124 ScriptNode fDef = null;
125 double rc, ic;
126 double dr;
127 Complex R;
128 int dimx, dimy;
129 int c = Arguments.Length;
130 int i = 0;
131 object Obj;
132
133 Obj = Arguments[i++].AssociatedObjectValue;
134 if (Obj is Complex z)
135 {
136 rc = z.Real;
137 ic = z.Imaginary;
138 }
139 else
140 {
141 rc = Expression.ToDouble(Obj);
142 ic = Expression.ToDouble(Arguments[i++].AssociatedObjectValue);
143 }
144
145 if (i >= c)
146 throw new ScriptRuntimeException("Insufficient parameters in call to HalleyTopographyFractal().", this);
147
148 dr = Expression.ToDouble(Arguments[i++].AssociatedObjectValue);
149
150 if (i < c && ((Obj = Arguments[i].AssociatedObjectValue) is double || Obj is Complex))
151 {
152 R = Expression.ToComplex(Obj);
153 i++;
154 }
155 else
156 {
157 R = Complex.One;
158
159 if (i < c && this.Arguments[i] is null)
160 i++;
161 }
162
163 if (i < c)
164 {
165 if (Arguments[i] is DoubleVector)
166 Coefficients = (double[])Arguments[i++].AssociatedObjectValue;
167 else if (Arguments[i] is ComplexVector)
168 CoefficientsZ = (Complex[])Arguments[i++].AssociatedObjectValue;
169 /*else if (Parameters[i] is RealPolynomial)
170 Coefficients = ((RealPolynomial)Arguments[i++].AssociatedObjectValue).Coefficients;
171 else if (Parameters[i] is ComplexPolynomial)
172 CoefficientsZ = ((ComplexPolynomial)Arguments[i++].AssociatedObjectValue).Coefficients;*/
173 else if (Arguments[i] is IVector)
174 {
175 IVector Vector = (IVector)Arguments[i++];
176 int j, d = Vector.Dimension;
177
178 CoefficientsZ = new Complex[d];
179 for (j = 0; j < d; j++)
180 CoefficientsZ[j] = Expression.ToComplex(Vector.GetElement(j).AssociatedObjectValue);
181 }
182 else if (Arguments[i].AssociatedObjectValue is ILambdaExpression)
183 {
184 f = (ILambdaExpression)Arguments[i];
185 if (f.NrArguments != 1)
186 throw new ScriptRuntimeException("Lambda expression in calls to HalleyTopographyFractal() must be of one variable.", this);
187
188 fDef = this.Arguments[i++];
189 }
190 else
191 {
192 throw new ScriptRuntimeException("Parameter " + (i + 1).ToString() +
193 " in call to HalleyTopographyFractal has to be a vector of numbers, containing coefficients " +
194 "of the polynomial to use. Now it was of type " + Arguments[i].GetType().FullName,
195 this);
196 }
197 }
198 else
199 throw new ScriptRuntimeException("Missing coefficients or lambda expression.", this);
200
201 if (i < c && !(this.Arguments[i] is null) && Arguments[i] is ObjectVector)
202 {
203 ColorExpression = this.Arguments[i].SubExpression;
204 Palette = FractalGraph.ToPalette((ObjectVector)Arguments[i++]);
205 }
206 else
207 {
208 Palette = ColorModels.RandomLinearAnalogousHSL.CreatePalette(128, 4, out int Seed, this, Variables);
209 ColorExpression = "RandomLinearAnalogousHSL(128,4," + Seed.ToString() + ")";
210
211 if (i < c && this.Arguments[i] is null)
212 i++;
213 }
214
215 if (i < c)
216 dimx = (int)Expression.ToDouble(Arguments[i++].AssociatedObjectValue);
217 else
218 dimx = 320;
219
220 if (i < c)
221 dimy = (int)Expression.ToDouble(Arguments[i++].AssociatedObjectValue);
222 else
223 dimy = 200;
224
225 if (i < c)
226 {
227 throw new ScriptRuntimeException("Parameter mismatch in call to HalleyTopographyFractal(z,dr[,R][,Coefficients][,Palette][,dimx[,dimy]]).",
228 this);
229 }
230
231 if (dimx <= 0 || dimx > 5000 || dimy <= 0 || dimy > 5000)
232 throw new ScriptRuntimeException("Image size must be within 1x1 to 5000x5000", this);
233
234 if (!(f is null))
235 {
236 return CalcHalley(rc, ic, dr, R, f, Variables, Palette, dimx, dimy, this, this.FractalZoomScript,
237 new object[] { Palette, dimx, dimy, R, fDef, ColorExpression });
238 }
239 else if (!(CoefficientsZ is null))
240 {
241 return CalcHalley(Variables, rc, ic, dr, R, CoefficientsZ, Palette, dimx, dimy,
242 this, this.FractalZoomScript,
243 new object[] { Palette, dimx, dimy, R, CoefficientsZ, ColorExpression });
244 }
245 else
246 {
247 return CalcHalley(Variables, rc, ic, dr, R, Coefficients, Palette, dimx, dimy,
248 this, this.FractalZoomScript,
249 new object[] { Palette, dimx, dimy, R, Coefficients, ColorExpression });
250 }
251 }
252
253 private string FractalZoomScript(double r, double i, double Size, object State)
254 {
255 object[] Parameters = (object[])State;
256 int DimX = (int)Parameters[1];
257 int DimY = (int)Parameters[2];
258 Complex R = (Complex)Parameters[3];
259 double[] Coefficients = Parameters[4] as double[];
260 string ColorExpression = (string)Parameters[5];
261
262 StringBuilder sb = new StringBuilder();
263
264 sb.Append("HalleyTopographyFractal((");
265 sb.Append(Expression.ToString(r));
266 sb.Append(',');
267 sb.Append(Expression.ToString(i));
268 sb.Append("),");
269 sb.Append(Expression.ToString(Size / 4));
270 sb.Append(',');
271 sb.Append(Expression.ToString(R));
272 sb.Append(',');
273
274 if (Parameters[4] is ScriptNode fDef)
275 sb.Append(fDef.SubExpression);
276 else if (Parameters[4] is Complex[] CoefficientsZ)
277 sb.Append(Expression.ToString(CoefficientsZ));
278 else
279 sb.Append(Expression.ToString(Coefficients));
280
281 if (!string.IsNullOrEmpty(ColorExpression))
282 {
283 sb.Append(',');
284 sb.Append(ColorExpression);
285 }
286
287 sb.Append(',');
288 sb.Append(DimX.ToString());
289 sb.Append(',');
290 sb.Append(DimY.ToString());
291 sb.Append(')');
292
293 return sb.ToString();
294 }
295
299 public static FractalGraph CalcHalley(Variables Variables, double rCenter, double iCenter, double rDelta, Complex R,
300 double[] Coefficients, SKColor[] Palette, int Width, int Height, ScriptNode Node,
301 FractalZoomScript FractalZoomScript, object State)
302 {
303 double RRe = R.Real;
304 double RIm = R.Imaginary;
305 double r0, i0, r1, i1;
306 double dr, di;
307 double r, i;
308 double zr, zi, zr2, zi2, zr3, zi3, zr4, zi4, zr5, zi5, zr6, zi6;
309 double aspect;
310 double Temp;
311 int x, y;
312 int n, N;
313 int index;
314 int Degree = Coefficients.Length - 1;
315
316 N = Palette.Length;
317
318 if (Degree < 3)
319 {
320 Array.Resize(ref Coefficients, 4);
321 while (Degree < 3)
322 Coefficients[++Degree] = 0;
323 }
324
325 double[] Prim = new double[Degree];
326 for (x = 1; x <= Degree; x++)
327 Prim[x - 1] = x * Coefficients[x];
328
329 double[] Bis = new double[Degree - 1];
330 for (x = 1; x < Degree; x++)
331 Bis[x - 1] = x * Prim[x];
332
333 Array.Reverse(Bis);
334 Array.Reverse(Prim);
335 Coefficients = (double[])Coefficients.Clone();
336 Array.Reverse(Coefficients);
337
338 int size = Width * Height;
339 int[] ColorIndex = new int[size];
340 double Conv = 1e-10;
341 double Div = 1e10;
342
343 rDelta *= 0.5;
344 r0 = rCenter - rDelta;
345 r1 = rCenter + rDelta;
346
347 aspect = ((double)Width) / Height;
348
349 i0 = iCenter - rDelta / aspect;
350 i1 = iCenter + rDelta / aspect;
351
352 dr = (r1 - r0) / Width;
353 di = (i1 - i0) / Height;
354
355 for (y = 0, i = i0, index = 0; y < Height; y++, i += di)
356 {
357 for (x = 0, r = r0; x < Width; x++, r += dr)
358 {
359 zr = r;
360 zi = i;
361
362 n = 0;
363 do
364 {
365 // f:
366 zr2 = zi2 = 0;
367 foreach (double C in Coefficients)
368 {
369 Temp = zr2 * zr - zi2 * zi + C;
370 zi2 = zr2 * zi + zi2 * zr;
371 zr2 = Temp;
372 }
373
374 // f':
375 zr3 = zi3 = 0;
376 foreach (double C in Prim)
377 {
378 Temp = zr3 * zr - zi3 * zi + C;
379 zi3 = zr3 * zi + zi3 * zr;
380 zr3 = Temp;
381 }
382
383 // f":
384 zr4 = zi4 = 0;
385 foreach (double C in Bis)
386 {
387 Temp = zr4 * zr - zi4 * zi + C;
388 zi4 = zr4 * zi + zi4 * zr;
389 zr4 = Temp;
390 }
391
392 // 2*f*f'
393
394 zr5 = 2 * (zr2 * zr3 - zi2 * zi3);
395 zi5 = 2 * (zr2 * zi3 + zi2 * zr3);
396
397 // 2f'^2-f*f"
398
399 zr6 = 2 * (zr3 * zr3 - zi3 * zi3) - (zr2 * zr4 - zi2 * zi4);
400 zi6 = 4 * zr3 * zi3 - (zr2 * zi4 + zr4 * zi2);
401
402 // R*2*f*f'/2f'^2-f*f"
403
404 Temp = 1.0 / (zr6 * zr6 + zi6 * zi6);
405 zr4 = (zr5 * zr6 + zi5 * zi6) * Temp;
406 zi4 = (zi5 * zr6 - zr5 * zi6) * Temp;
407
408 // R*2*f*f'/(2f'^2-f*f")
409 Temp = zr4 * RRe - zi4 * RIm;
410 zi4 = zr4 * RIm + zi4 * RRe;
411 zr4 = Temp;
412
413 zr -= zr4;
414 zi -= zi4;
415
416 Temp = Math.Sqrt(zr4 * zr4 + zi4 * zi4);
417 }
418 while ((Temp > Conv) && (Temp < Div) && (n++ < N));
419
420 if (Temp < Conv && n < N)
421 ColorIndex[index++] = n;
422 else
423 ColorIndex[index++] = N;
424 }
425 }
426
427 ColorIndex = FractalGraph.FindBoundaries(ColorIndex, Width, Height);
428
429 return new FractalGraph(Variables, FractalGraph.ToPixels(ColorIndex, Width, Height, Palette),
430 r0, i0, r1, i1, rDelta * 2, true, Node, FractalZoomScript, State);
431 }
432
436 public static FractalGraph CalcHalley(Variables Variables, double rCenter, double iCenter, double rDelta, Complex R,
437 Complex[] Coefficients, SKColor[] Palette, int Width, int Height, ScriptNode Node, FractalZoomScript FractalZoomScript,
438 object State)
439 {
440 double RRe = R.Real;
441 double RIm = R.Imaginary;
442 double r0, i0, r1, i1;
443 double dr, di;
444 double r, i;
445 double zr, zi, zr2, zi2, zr3, zi3, zr4, zi4, zr5, zi5, zr6, zi6;
446 double aspect;
447 double Temp;
448 int x, y;
449 int n, N;
450 int index;
451 int Degree = Coefficients.Length - 1;
452
453 N = Palette.Length;
454
455 if (Degree < 3)
456 {
457 Array.Resize(ref Coefficients, 4);
458 while (Degree < 3)
459 Coefficients[++Degree] = Complex.Zero;
460 }
461
462 Complex[] Prim = new Complex[Degree];
463 for (x = 1; x <= Degree; x++)
464 Prim[x - 1] = x * Coefficients[x];
465
466 Complex[] Bis = new Complex[Degree - 1];
467 for (x = 1; x < Degree; x++)
468 Bis[x - 1] = x * Prim[x];
469
470 Array.Reverse(Bis);
471 Array.Reverse(Prim);
472 Coefficients = (Complex[])Coefficients.Clone();
473 Array.Reverse(Coefficients);
474
475 int j, c = Prim.Length;
476 int c2 = c - 1;
477 double[] ReC = new double[c + 1];
478 double[] ImC = new double[c + 1];
479 double[] RePrim = new double[c];
480 double[] ImPrim = new double[c];
481 double[] ReBis = new double[c2];
482 double[] ImBis = new double[c2];
483 Complex z;
484
485 for (j = 0; j < c; j++)
486 {
487 z = Coefficients[j];
488 ReC[j] = z.Real;
489 ImC[j] = z.Imaginary;
490
491 z = Prim[j];
492 RePrim[j] = z.Real;
493 ImPrim[j] = z.Imaginary;
494
495 if (j < c2)
496 {
497 z = Bis[j];
498 ReBis[j] = z.Real;
499 ImBis[j] = z.Imaginary;
500 }
501 }
502
503 z = Coefficients[j];
504 ReC[j] = z.Real;
505 ImC[j] = z.Imaginary;
506
507 int size = Width * Height;
508 int[] ColorIndex = new int[size];
509 double Conv = 1e-10;
510 double Div = 1e10;
511
512 rDelta *= 0.5;
513 r0 = rCenter - rDelta;
514 r1 = rCenter + rDelta;
515
516 aspect = ((double)Width) / Height;
517
518 i0 = iCenter - rDelta / aspect;
519 i1 = iCenter + rDelta / aspect;
520
521 dr = (r1 - r0) / Width;
522 di = (i1 - i0) / Height;
523
524 for (y = 0, i = i0, index = 0; y < Height; y++, i += di)
525 {
526 for (x = 0, r = r0; x < Width; x++, r += dr)
527 {
528 zr = r;
529 zi = i;
530
531 n = 0;
532 do
533 {
534 // f:
535 zr2 = zi2 = 0;
536 for (j = 0; j <= c; j++)
537 {
538 Temp = zr2 * zr - zi2 * zi + ReC[j];
539 zi2 = zr2 * zi + zi2 * zr + ImC[j];
540 zr2 = Temp;
541 }
542
543 // f':
544 zr3 = zi3 = 0;
545 for (j = 0; j < c; j++)
546 {
547 Temp = zr3 * zr - zi3 * zi + RePrim[j];
548 zi3 = zr3 * zi + zi3 * zr + ImPrim[j];
549 zr3 = Temp;
550 }
551
552 // f":
553 zr4 = zi4 = 0;
554 for (j = 0; j < c2; j++)
555 {
556 Temp = zr4 * zr - zi4 * zi + ReBis[j];
557 zi4 = zr4 * zi + zi4 * zr + ImBis[j];
558 zr4 = Temp;
559 }
560
561 // 2*f*f'
562
563 zr5 = 2 * (zr2 * zr3 - zi2 * zi3);
564 zi5 = 2 * (zr2 * zi3 + zi2 * zr3);
565
566 // 2f'^2-f*f"
567
568 zr6 = 2 * (zr3 * zr3 - zi3 * zi3) - (zr2 * zr4 - zi2 * zi4);
569 zi6 = 4 * zr3 * zi3 - (zr2 * zi4 + zr4 * zi2);
570
571 // R*2*f*f'/2f'^2-f*f"
572
573 Temp = 1.0 / (zr6 * zr6 + zi6 * zi6);
574 zr4 = (zr5 * zr6 + zi5 * zi6) * Temp;
575 zi4 = (zi5 * zr6 - zr5 * zi6) * Temp;
576
577 // R*2*f*f'/(2f'^2-f*f")
578 Temp = zr4 * RRe - zi4 * RIm;
579 zi4 = zr4 * RIm + zi4 * RRe;
580 zr4 = Temp;
581
582 zr -= zr4;
583 zi -= zi4;
584
585 Temp = Math.Sqrt(zr4 * zr4 + zi4 * zi4);
586 }
587 while ((Temp > Conv) && (Temp < Div) && (n++ < N));
588
589 if (Temp < Conv && n < N)
590 ColorIndex[index++] = n;
591 else
592 ColorIndex[index++] = N;
593 }
594 }
595
596 ColorIndex = FractalGraph.FindBoundaries(ColorIndex, Width, Height);
597
598 return new FractalGraph(Variables, FractalGraph.ToPixels(ColorIndex, Width, Height, Palette),
599 r0, i0, r1, i1, rDelta * 2, true, Node, FractalZoomScript, State);
600 }
601
605 public static FractalGraph CalcHalley(double rCenter, double iCenter, double rDelta, Complex R,
606 ILambdaExpression f, Variables Variables, SKColor[] Palette, int Width, int Height,
607 ScriptNode Node, FractalZoomScript FractalZoomScript, object State)
608 {
609 double RRe = R.Real;
610 double RIm = R.Imaginary;
611 double r0, i0, r1, i1;
612 double dr, di;
613 double r, i;
614 double aspect;
615 int x, y;
616 int n, N;
617
618 N = Palette.Length;
619
620 Variables v = new Variables();
621 Variables.CopyTo(v);
622
623 string ParameterName;
624 if (!(f is IDifferentiable Differentiable) ||
625 !(Differentiable.Differentiate(ParameterName = Differentiable.DefaultVariableName, v) is ILambdaExpression fPrim))
626 {
627 throw new ScriptRuntimeException("Lambda expression not differentiable.", Node);
628 }
629
630 if (!(fPrim is IDifferentiable Differentiable2) ||
631 !(Differentiable2.Differentiate(ParameterName, v) is ILambdaExpression fBis))
632 {
633 throw new ScriptRuntimeException("Lambda expression not twice differentiable.", Node);
634 }
635
636 int size = Width * Height;
637 int[] ColorIndex = new int[size];
638 double Conv = 1e-10;
639 double Div = 1e10;
640
641 Complex[] Row;
642 Complex[] Row2;
643 Complex[] Row3;
644 Complex[] Row4;
645 int[] Offset;
646 IElement[] P = new IElement[1];
647 int j, c, x2;
648 IElement Obj, Obj2, Obj3;
649 double Mod;
650 Complex z, z2, z3;
651 Complex R2 = R * 2;
652
653 rDelta *= 0.5;
654 r0 = rCenter - rDelta;
655 r1 = rCenter + rDelta;
656
657 aspect = ((double)Width) / Height;
658
659 i0 = iCenter - rDelta / aspect;
660 i1 = iCenter + rDelta / aspect;
661
662 dr = (r1 - r0) / Width;
663 di = (i1 - i0) / Height;
664
665 for (y = 0, i = i0; y < Height; y++, i += di)
666 {
667 Row = new Complex[Width];
668 Offset = new int[Width];
669
670 c = Width;
671 for (x = 0, x2 = y * Width, r = r0; x < Width; x++, r += dr, x2++)
672 {
673 Row[x] = new Complex(r, i);
674 Offset[x] = x2;
675 }
676
677 n = 0;
678 while (n < N && c > 0)
679 {
680 n++;
681 P[0] = new ComplexVector(Row);
682 Obj = f.Evaluate(P, v);
683 Obj2 = fPrim.Evaluate(P, v);
684 Obj3 = fBis.Evaluate(P, v);
685 Row2 = Obj.AssociatedObjectValue as Complex[];
686 Row3 = Obj2.AssociatedObjectValue as Complex[];
687 Row4 = Obj3.AssociatedObjectValue as Complex[];
688
689 if (Row2 is null || Row3 is null || Row4 is null)
690 {
691 throw new ScriptRuntimeException("Lambda expression (and its first and second derivative) must be able to accept complex vectors, " +
692 "and return complex vectors of equal length. Type returned: " +
693 Obj.GetType().FullName + ", " + Obj2.GetType().FullName + " and " + Obj3.GetType().FullName,
694 Node);
695 }
696 else if (Row2.Length != c || Row3.Length != c)
697 {
698 throw new ScriptRuntimeException("Lambda expression (and its first and second derivative) must be able to accept complex vectors, " +
699 "and return complex vectors of equal length. Length returned: " +
700 Row2.Length.ToString() + ", " + Row3.Length.ToString() + " and " + Row4.Length.ToString() +
701 ". Expected: " + c.ToString(), Node);
702 }
703
704 for (x = x2 = 0; x < c; x++)
705 {
706 j = Offset[x];
707 z = Row2[x];
708 z2 = Row3[x];
709 z3 = Row4[x];
710
711 z = R2 * z * z2 / (2 * z2 * z2 - z * z3);
712 Row[x] -= z;
713
714 Mod = z.Magnitude;
715
716 if (Mod > Conv && Mod < Div)
717 {
718 if (x != x2)
719 Offset[x2] = j;
720
721 x2++;
722 }
723 else
724 {
725 if (n >= N)
726 ColorIndex[j++] = N;
727 else
728 ColorIndex[j++] = n;
729 }
730 }
731
732 if (x2 < x)
733 {
734 Array.Resize(ref Row, x2);
735 Array.Resize(ref Offset, x2);
736 c = x2;
737 }
738 }
739 }
740
741 ColorIndex = FractalGraph.FindBoundaries(ColorIndex, Width, Height);
742
743 return new FractalGraph(Variables, FractalGraph.ToPixels(ColorIndex, Width, Height, Palette),
744 r0, i0, r1, i1, rDelta * 2, true, Node, FractalZoomScript, State);
745 }
746
750 public override string FunctionName => nameof(HalleyTopographyFractal);
751 }
752}
Waher.Script.Expression
Class managing a script expression.
Definition: Expression.cs:39
Waher.Script.Expression.ToComplex
static Complex ToComplex(object Object)
Converts an object to a complex value.
Definition: Expression.cs:4942
Waher.Script.Expression.ToDouble
static double ToDouble(object Object)
Converts an object to a double value.
Definition: Expression.cs:4824
Waher.Script.Expression.ToString
static string ToString(double Value)
Converts a value to a string, that can be parsed as part of an expression.
Definition: Expression.cs:4496
Waher.Script.Fractals.ComplexFractals.HalleyTopographyFractal.HalleyTopographyFractal
HalleyTopographyFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode Coefficients, int Start, int Length, Expression Expression)
TODO
Definition: HalleyTopographyFractal.cs:77
Waher.Script.Fractals.ComplexFractals.HalleyTopographyFractal.HalleyTopographyFractal
HalleyTopographyFractal(ScriptNode z, ScriptNode dr, int Start, int Length, Expression Expression)
TODO
Definition: HalleyTopographyFractal.cs:97
Waher.Script.Fractals.ComplexFractals.HalleyTopographyFractal.HalleyTopographyFractal
HalleyTopographyFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode Coefficients, ScriptNode Palette, ScriptNode DimX, ScriptNode DimY, int Start, int Length, Expression Expression)
TODO
Definition: HalleyTopographyFractal.cs:44
Waher.Script.Fractals.ComplexFractals.HalleyTopographyFractal.Evaluate
override IElement Evaluate(IElement[] Arguments, Variables Variables)
TODO
Definition: HalleyTopographyFractal.cs:117
Waher.Script.Fractals.ComplexFractals.HalleyTopographyFractal.HalleyTopographyFractal
HalleyTopographyFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode Coefficients, ScriptNode Palette, ScriptNode DimX, int Start, int Length, Expression Expression)
TODO
Definition: HalleyTopographyFractal.cs:55
Waher.Script.Fractals.ComplexFractals.HalleyTopographyFractal.CalcHalley
static FractalGraph CalcHalley(Variables Variables, double rCenter, double iCenter, double rDelta, Complex R, double[] Coefficients, SKColor[] Palette, int Width, int Height, ScriptNode Node, FractalZoomScript FractalZoomScript, object State)
TODO
Definition: HalleyTopographyFractal.cs:299
Waher.Script.Fractals.ComplexFractals.HalleyTopographyFractal.HalleyTopographyFractal
HalleyTopographyFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode Coefficients, ScriptNode Palette, int Start, int Length, Expression Expression)
TODO
Definition: HalleyTopographyFractal.cs:66
Waher.Script.Fractals.ComplexFractals.HalleyTopographyFractal.CalcHalley
static FractalGraph CalcHalley(Variables Variables, double rCenter, double iCenter, double rDelta, Complex R, Complex[] Coefficients, SKColor[] Palette, int Width, int Height, ScriptNode Node, FractalZoomScript FractalZoomScript, object State)
TODO
Definition: HalleyTopographyFractal.cs:436
Waher.Script.Fractals.ComplexFractals.HalleyTopographyFractal.CalcHalley
static FractalGraph CalcHalley(double rCenter, double iCenter, double rDelta, Complex R, ILambdaExpression f, Variables Variables, SKColor[] Palette, int Width, int Height, ScriptNode Node, FractalZoomScript FractalZoomScript, object State)
TODO
Definition: HalleyTopographyFractal.cs:605
Waher.Script.Fractals.ComplexFractals.HalleyTopographyFractal.HalleyTopographyFractal
HalleyTopographyFractal(ScriptNode z, ScriptNode dr, ScriptNode R, int Start, int Length, Expression Expression)
TODO
Definition: HalleyTopographyFractal.cs:88
Waher.Script.Fractals.FractalGraph
Defines a clickable fractal graph in the complex plane.
Definition: FractalGraph.cs:22
Waher.Script.Fractals.FractalGraph.ToPixels
static PixelInformation ToPixels(double[] ColorIndex, int Width, int Height, SKColor[] Palette)
TODO
Definition: FractalGraph.cs:1118
Waher.Script.Fractals.FractalGraph.ToPalette
static SKColor[] ToPalette(ObjectVector Vector)
TODO
Definition: FractalGraph.cs:101
Waher.Script.Fractals.FractalGraph.FindBoundaries
static double[] FindBoundaries(double[] ColorIndex, int Width, int Height)
TODO
Definition: FractalGraph.cs:371
Waher.Script.Model.FunctionMultiVariate
Base class for multivariate funcions.
Definition: FunctionMultiVariate.cs:15
Waher.Script.Model.FunctionMultiVariate.Arguments
ScriptNode[] Arguments
Function arguments.
Definition: FunctionMultiVariate.cs:183
Waher.Script.Model.ScriptNode
Base class for all nodes in a parsed script tree.
Definition: ScriptNode.cs:69
Waher.Script.Model.ScriptNode.Length
int Length
Length of expression covered by node.
Definition: ScriptNode.cs:101
Waher.Script.Model.ScriptNode.ToString
override string ToString()
Definition: ScriptNode.cs:359
Waher.Script.Model.ScriptNode.Expression
Expression Expression
Expression of which the node is a part.
Definition: ScriptNode.cs:177
Waher.Script.Model.ScriptNode.Start
int Start
Start position in script expression.
Definition: ScriptNode.cs:92
Waher.Script.Variables
Collection of variables.
Definition: Variables.cs:25
Waher.Script.Variables.CopyTo
void CopyTo(Variables Variables)
Copies available variables to another variable collection.
Definition: Variables.cs:400
Waher.Script.Abstraction.Elements.IElement
Basic interface for all types of elements.
Definition: IElement.cs:20
Waher.Script.Abstraction.Elements.IElement.AssociatedObjectValue
object AssociatedObjectValue
Associated object value.
Definition: IElement.cs:33
Waher.Script.Abstraction.Elements.IVector
Basic interface for vectors.
Definition: IVector.cs:9
Waher.Script.Abstraction.Elements.IVector.Dimension
int Dimension
Dimension of vector.
Definition: IVector.cs:14
Waher.Script.Abstraction.Elements.IVector.GetElement
IElement GetElement(int Index)
Gets an element of the vector.
Waher.Script.Model.IDifferentiable
Base interface for lambda expressions.
Definition: IDifferentiable.cs:9
Waher.Script.Model.ILambdaExpression
Base interface for lambda expressions.
Definition: ILambdaExpression.cs:11
Waher.Script.Model.ILambdaExpression.Evaluate
IElement Evaluate(IElement[] Arguments, Variables Variables)
Evaluates the lambda expression.
Waher.Script.Fractals.FractalZoomScript
delegate string FractalZoomScript(double r, double i, double Size, object State)
Generates new script when zoomed.
Waher.Script.Model.ArgumentType
ArgumentType
Type of parameter used in a function definition or a lambda definition.
Definition: IFunction.cs:9