Neuron®
The Neuron® is the basis for the creation of open and secure federated networks for smart societies.
Loading...
Searching...
No Matches
HalleyFractal.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.Graphs;
9using Waher.Script.Objects.VectorSpaces;
10
11namespace Waher.Script.Fractals.ComplexFractals
12{
42 public class HalleyFractal : FunctionMultiVariate
43 {
47 public HalleyFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode Coefficients,
48 ScriptNode Palette, ScriptNode DimX, ScriptNode DimY, int Start, int Length, Expression Expression)
49 : base(new ScriptNode[] { z, dr, R, Coefficients, Palette, DimX, DimY },
50 new ArgumentType[] { ArgumentType.Scalar, ArgumentType.Scalar, ArgumentType.Scalar,
51 ArgumentType.Normal, ArgumentType.Vector, ArgumentType.Scalar, ArgumentType.Scalar}, Start, Length, Expression)
52 {
53 }
54
58 public HalleyFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode Coefficients,
59 ScriptNode Palette, ScriptNode DimX, int Start, int Length, Expression Expression)
60 : base(new ScriptNode[] { z, dr, R, Coefficients, Palette, DimX },
61 new ArgumentType[] { ArgumentType.Scalar, ArgumentType.Scalar, ArgumentType.Scalar,
62 ArgumentType.Normal, ArgumentType.Vector, ArgumentType.Scalar}, Start, Length, Expression)
63 {
64 }
65
69 public HalleyFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode Coefficients,
70 ScriptNode Palette, int Start, int Length, Expression Expression)
71 : base(new ScriptNode[] { z, dr, R, Coefficients, Palette },
72 new ArgumentType[] { ArgumentType.Scalar, ArgumentType.Scalar, ArgumentType.Scalar,
73 ArgumentType.Normal, ArgumentType.Vector}, Start, Length, Expression)
74 {
75 }
76
80 public HalleyFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode Coefficients,
81 int Start, int Length, Expression Expression)
82 : base(new ScriptNode[] { z, dr, R, Coefficients },
83 new ArgumentType[] { ArgumentType.Scalar, ArgumentType.Scalar, ArgumentType.Scalar,
84 ArgumentType.Normal}, Start, Length, Expression)
85 {
86 }
87
91 public HalleyFractal(ScriptNode z, ScriptNode dr, ScriptNode R, int Start, int Length, Expression Expression)
92 : base(new ScriptNode[] { z, dr, R },
93 new ArgumentType[] { ArgumentType.Scalar, ArgumentType.Scalar, ArgumentType.Scalar }, Start, Length, Expression)
94 {
95 }
96
100 public HalleyFractal(ScriptNode z, ScriptNode dr, int Start, int Length, Expression Expression)
101 : base(new ScriptNode[] { z, dr },
102 new ArgumentType[] { ArgumentType.Scalar, ArgumentType.Scalar }, Start, Length, Expression)
103 {
104 }
105
109 public override string[] DefaultArgumentNames
110 {
111 get
112 {
113 return new string[] { "z", "dr", "R", "Coefficients", "Palette", "DimX", "DimY" };
114 }
115 }
116
120 public override IElement Evaluate(IElement[] Arguments, Variables Variables)
121 {
122 string ColorExpression = null;
123 SKColor[] Palette;
124 double[] Coefficients = null;
125 Complex[] CoefficientsZ = null;
126 ILambdaExpression f = null;
127 ScriptNode fDef = null;
128 double rc, ic;
129 double dr;
130 Complex R;
131 int dimx, dimy;
132 int c = Arguments.Length;
133 int i = 0;
134 object Obj;
135
136 Obj = Arguments[i++].AssociatedObjectValue;
137 if (Obj is Complex z)
138 {
139 rc = z.Real;
140 ic = z.Imaginary;
141 }
142 else
143 {
144 rc = Expression.ToDouble(Obj);
145 ic = Expression.ToDouble(Arguments[i++].AssociatedObjectValue);
146 }
147
148 if (i >= c)
149 throw new ScriptRuntimeException("Insufficient parameters in call to HalleyFractal().", this);
150
151 dr = Expression.ToDouble(Arguments[i++].AssociatedObjectValue);
152
153 if (i < c && ((Obj = Arguments[i].AssociatedObjectValue) is double || Obj is Complex))
154 {
155 R = Expression.ToComplex(Obj);
156 i++;
157 }
158 else
159 {
160 R = Complex.One;
161
162 if (i < c && this.Arguments[i] is null)
163 i++;
164 }
165
166 if (i < c)
167 {
168 if (Arguments[i] is DoubleVector)
169 Coefficients = (double[])Arguments[i++].AssociatedObjectValue;
170 else if (Arguments[i] is ComplexVector)
171 CoefficientsZ = (Complex[])Arguments[i++].AssociatedObjectValue;
172 /*else if (Parameters[i] is RealPolynomial)
173 Coefficients = ((RealPolynomial)Arguments[i++].AssociatedObjectValue).Coefficients;
174 else if (Parameters[i] is ComplexPolynomial)
175 CoefficientsZ = ((ComplexPolynomial)Arguments[i++].AssociatedObjectValue).Coefficients;*/
176 else if (Arguments[i] is IVector)
177 {
178 IVector Vector = (IVector)Arguments[i++];
179 int j, d = Vector.Dimension;
180
181 CoefficientsZ = new Complex[d];
182 for (j = 0; j < d; j++)
183 CoefficientsZ[j] = Expression.ToComplex(Vector.GetElement(j).AssociatedObjectValue);
184 }
185 else if (Arguments[i].AssociatedObjectValue is ILambdaExpression)
186 {
187 f = (ILambdaExpression)Arguments[i];
188 if (f.NrArguments != 1)
189 throw new ScriptRuntimeException("Lambda expression in calls to HalleyFractal() must be of one variable.", this);
190
191 fDef = this.Arguments[i++];
192 }
193 else
194 {
195 throw new ScriptRuntimeException("Parameter " + (i + 1).ToString() +
196 " in call to HalleyFractal has to be a vector of numbers, containing coefficients " +
197 "of the polynomial to use. Now it was of type " + Arguments[i].GetType().FullName,
198 this);
199 }
200 }
201 else
202 throw new ScriptRuntimeException("Missing coefficients or lambda expression.", this);
203
204 if (i < c && !(this.Arguments[i] is null) && Arguments[i] is ObjectVector)
205 {
206 ColorExpression = this.Arguments[i].SubExpression;
207 Palette = FractalGraph.ToPalette((ObjectVector)Arguments[i++]);
208 }
209 else
210 {
211 Palette = ColorModels.RandomLinearAnalogousHSL.CreatePalette(128, 4, out int Seed, this, Variables);
212 ColorExpression = "RandomLinearAnalogousHSL(128,4," + Seed.ToString() + ")";
213
214 if (i < c && this.Arguments[i] is null)
215 i++;
216 }
217
218 if (i < c)
219 dimx = (int)Expression.ToDouble(Arguments[i++].AssociatedObjectValue);
220 else
221 dimx = 320;
222
223 if (i < c)
224 dimy = (int)Expression.ToDouble(Arguments[i++].AssociatedObjectValue);
225 else
226 dimy = 200;
227
228 if (i < c)
229 {
230 throw new ScriptRuntimeException("Parameter mismatch in call to HalleyFractal(z,dr[,R][,Coefficients][,Palette][,dimx[,dimy]]).",
231 this);
232 }
233
234 if (dimx <= 0 || dimx > 5000 || dimy <= 0 || dimy > 5000)
235 throw new ScriptRuntimeException("Image size must be within 1x1 to 5000x5000", this);
236
237 if (!(f is null))
238 {
239 return CalcHalley(Variables, rc, ic, dr, R, f, fDef, Palette, dimx, dimy,
240 this, this.FractalZoomScript,
241 new object[] { Palette, dimx, dimy, R, fDef, ColorExpression });
242 }
243 else if (!(CoefficientsZ is null))
244 {
245 return CalcHalley(Variables, rc, ic, dr, R, CoefficientsZ, Palette, dimx, dimy,
246 this, this.FractalZoomScript,
247 new object[] { Palette, dimx, dimy, R, CoefficientsZ, ColorExpression });
248 }
249 else
250 {
251 return CalcHalley(Variables, rc, ic, dr, R, Coefficients, Palette, dimx, dimy,
252 this, this.FractalZoomScript,
253 new object[] { Palette, dimx, dimy, R, Coefficients, ColorExpression });
254 }
255 }
256
257 private string FractalZoomScript(double r, double i, double Size, object State)
258 {
259 object[] Parameters = (object[])State;
260 int DimX = (int)Parameters[1];
261 int DimY = (int)Parameters[2];
262 Complex R = (Complex)Parameters[3];
263 double[] Coefficients = Parameters[4] as double[];
264 string ColorExpression = (string)Parameters[5];
265
266 StringBuilder sb = new StringBuilder();
267
268 sb.Append("HalleyFractal((");
269 sb.Append(Expression.ToString(r));
270 sb.Append(',');
271 sb.Append(Expression.ToString(i));
272 sb.Append("),");
273 sb.Append(Expression.ToString(Size / 4));
274 sb.Append(',');
275 sb.Append(Expression.ToString(R));
276 sb.Append(',');
277
278 if (Parameters[4] is ScriptNode fDef)
279 sb.Append(fDef.SubExpression);
280 else if (Parameters[4] is Complex[] CoefficientsZ)
281 sb.Append(Expression.ToString(CoefficientsZ));
282 else
283 sb.Append(Expression.ToString(Coefficients));
284
285 if (!string.IsNullOrEmpty(ColorExpression))
286 {
287 sb.Append(',');
288 sb.Append(ColorExpression);
289 }
290
291 sb.Append(',');
292 sb.Append(DimX.ToString());
293 sb.Append(',');
294 sb.Append(DimY.ToString());
295 sb.Append(')');
296
297 return sb.ToString();
298 }
299
315 public static FractalGraph CalcHalley(Variables Variables, double rCenter, double iCenter, double rDelta, Complex R,
316 double[] Coefficients, SKColor[] Palette, int Width, int Height, ScriptNode Node,
317 FractalZoomScript FractalZoomScript, object State)
318 {
319 byte[] reds;
320 byte[] greens;
321 byte[] blues;
322 double RRe = R.Real;
323 double RIm = R.Imaginary;
324 double r0, i0, r1, i1;
325 double dr, di;
326 double r, i;
327 double zr, zi, zr2, zi2, zr3, zi3, zr4, zi4, zr5, zi5, zr6, zi6;
328 double aspect;
329 double Temp;
330 int x, y;
331 int n, N;
332 int index;
333 int Degree = Coefficients.Length - 1;
334 SKColor cl;
335
336 N = Palette.Length;
337 reds = new byte[N];
338 greens = new byte[N];
339 blues = new byte[N];
340
341 for (x = 0; x < N; x++)
342 {
343 cl = Palette[x];
344 reds[x] = cl.Red;
345 greens[x] = cl.Green;
346 blues[x] = cl.Blue;
347 }
348
349 if (Degree < 3)
350 {
351 Array.Resize(ref Coefficients, 4);
352 while (Degree < 3)
353 Coefficients[++Degree] = 0;
354 }
355
356 double[] Prim = new double[Degree];
357 for (x = 1; x <= Degree; x++)
358 Prim[x - 1] = x * Coefficients[x];
359
360 double[] Bis = new double[Degree - 1];
361 for (x = 1; x < Degree; x++)
362 Bis[x - 1] = x * Prim[x];
363
364 Array.Reverse(Bis);
365 Array.Reverse(Prim);
366 Coefficients = (double[])Coefficients.Clone();
367 Array.Reverse(Coefficients);
368
369 int size = Width * Height * 4;
370 double Conv = 1e-10;
371 double Div = 1e10;
372 byte[] rgb = new byte[size];
373
374 rDelta *= 0.5;
375 r0 = rCenter - rDelta;
376 r1 = rCenter + rDelta;
377
378 aspect = ((double)Width) / Height;
379
380 i0 = iCenter - rDelta / aspect;
381 i1 = iCenter + rDelta / aspect;
382
383 dr = (r1 - r0) / Width;
384 di = (i1 - i0) / Height;
385
386 for (y = 0, i = i0, index = 0; y < Height; y++, i += di)
387 {
388 for (x = 0, r = r0; x < Width; x++, r += dr)
389 {
390 zr = r;
391 zi = i;
392
393 n = 0;
394 do
395 {
396 // f:
397 zr2 = zi2 = 0;
398 foreach (double C in Coefficients)
399 {
400 Temp = zr2 * zr - zi2 * zi + C;
401 zi2 = zr2 * zi + zi2 * zr;
402 zr2 = Temp;
403 }
404
405 // f':
406 zr3 = zi3 = 0;
407 foreach (double C in Prim)
408 {
409 Temp = zr3 * zr - zi3 * zi + C;
410 zi3 = zr3 * zi + zi3 * zr;
411 zr3 = Temp;
412 }
413
414 // f":
415 zr4 = zi4 = 0;
416 foreach (double C in Bis)
417 {
418 Temp = zr4 * zr - zi4 * zi + C;
419 zi4 = zr4 * zi + zi4 * zr;
420 zr4 = Temp;
421 }
422
423 // 2*f*f'
424
425 zr5 = 2 * (zr2 * zr3 - zi2 * zi3);
426 zi5 = 2 * (zr2 * zi3 + zi2 * zr3);
427
428 // 2f'^2-f*f"
429
430 zr6 = 2 * (zr3 * zr3 - zi3 * zi3) - (zr2 * zr4 - zi2 * zi4);
431 zi6 = 4 * zr3 * zi3 - (zr2 * zi4 + zr4 * zi2);
432
433 // R*2*f*f'/2f'^2-f*f"
434
435 Temp = 1.0 / (zr6 * zr6 + zi6 * zi6);
436 zr4 = (zr5 * zr6 + zi5 * zi6) * Temp;
437 zi4 = (zi5 * zr6 - zr5 * zi6) * Temp;
438
439 // R*2*f*f'/(2f'^2-f*f")
440 Temp = zr4 * RRe - zi4 * RIm;
441 zi4 = zr4 * RIm + zi4 * RRe;
442 zr4 = Temp;
443
444 zr -= zr4;
445 zi -= zi4;
446
447 Temp = Math.Sqrt(zr4 * zr4 + zi4 * zi4);
448 }
449 while ((Temp > Conv) && (Temp < Div) && (n++ < N));
450
451 if (Temp < Conv && n < N)
452 {
453 rgb[index++] = blues[n];
454 rgb[index++] = greens[n];
455 rgb[index++] = reds[n];
456 }
457 else
458 {
459 rgb[index++] = 0;
460 rgb[index++] = 0;
461 rgb[index++] = 0;
462 }
463
464 rgb[index++] = 255;
465 }
466 }
467
468 PixelInformation Pixels = new PixelInformationRaw(SKColorType.Bgra8888, rgb, Width, Height, Width << 2);
469 return new FractalGraph(Variables, Pixels, r0, i0, r1, i1, rDelta * 2, true, Node, FractalZoomScript, State);
470 }
471
475 public static FractalGraph CalcHalley(Variables Variables, double rCenter, double iCenter, double rDelta, Complex R,
476 Complex[] Coefficients, SKColor[] Palette, int Width, int Height, ScriptNode Node,
477 FractalZoomScript FractalZoomScript, object State)
478 {
479 byte[] reds;
480 byte[] greens;
481 byte[] blues;
482 double RRe = R.Real;
483 double RIm = R.Imaginary;
484 double r0, i0, r1, i1;
485 double dr, di;
486 double r, i;
487 double zr, zi, zr2, zi2, zr3, zi3, zr4, zi4, zr5, zi5, zr6, zi6;
488 double aspect;
489 double Temp;
490 int x, y;
491 int n, N;
492 int index;
493 int Degree = Coefficients.Length - 1;
494 SKColor cl;
495
496 N = Palette.Length;
497 reds = new byte[N];
498 greens = new byte[N];
499 blues = new byte[N];
500
501 for (x = 0; x < N; x++)
502 {
503 cl = Palette[x];
504 reds[x] = cl.Red;
505 greens[x] = cl.Green;
506 blues[x] = cl.Blue;
507 }
508
509 if (Degree < 3)
510 {
511 Array.Resize(ref Coefficients, 4);
512 while (Degree < 3)
513 Coefficients[++Degree] = Complex.Zero;
514 }
515
516 Complex[] Prim = new Complex[Degree];
517 for (x = 1; x <= Degree; x++)
518 Prim[x - 1] = x * Coefficients[x];
519
520 Complex[] Bis = new Complex[Degree - 1];
521 for (x = 1; x < Degree; x++)
522 Bis[x - 1] = x * Prim[x];
523
524 Array.Reverse(Bis);
525 Array.Reverse(Prim);
526 Coefficients = (Complex[])Coefficients.Clone();
527 Array.Reverse(Coefficients);
528
529 int j, c = Prim.Length;
530 int c2 = c - 1;
531 double[] ReC = new double[c + 1];
532 double[] ImC = new double[c + 1];
533 double[] RePrim = new double[c];
534 double[] ImPrim = new double[c];
535 double[] ReBis = new double[c2];
536 double[] ImBis = new double[c2];
537 Complex z;
538
539 for (j = 0; j < c; j++)
540 {
541 z = Coefficients[j];
542 ReC[j] = z.Real;
543 ImC[j] = z.Imaginary;
544
545 z = Prim[j];
546 RePrim[j] = z.Real;
547 ImPrim[j] = z.Imaginary;
548
549 if (j < c2)
550 {
551 z = Bis[j];
552 ReBis[j] = z.Real;
553 ImBis[j] = z.Imaginary;
554 }
555 }
556
557 z = Coefficients[j];
558 ReC[j] = z.Real;
559 ImC[j] = z.Imaginary;
560
561 int size = Width * Height * 4;
562 double Conv = 1e-10;
563 double Div = 1e10;
564 byte[] rgb = new byte[size];
565
566 rDelta *= 0.5;
567 r0 = rCenter - rDelta;
568 r1 = rCenter + rDelta;
569
570 aspect = ((double)Width) / Height;
571
572 i0 = iCenter - rDelta / aspect;
573 i1 = iCenter + rDelta / aspect;
574
575 dr = (r1 - r0) / Width;
576 di = (i1 - i0) / Height;
577
578 for (y = 0, i = i0, index = 0; y < Height; y++, i += di)
579 {
580 for (x = 0, r = r0; x < Width; x++, r += dr)
581 {
582 zr = r;
583 zi = i;
584
585 n = 0;
586 do
587 {
588 // f:
589 zr2 = zi2 = 0;
590 for (j = 0; j <= c; j++)
591 {
592 Temp = zr2 * zr - zi2 * zi + ReC[j];
593 zi2 = zr2 * zi + zi2 * zr + ImC[j];
594 zr2 = Temp;
595 }
596
597 // f':
598 zr3 = zi3 = 0;
599 for (j = 0; j < c; j++)
600 {
601 Temp = zr3 * zr - zi3 * zi + RePrim[j];
602 zi3 = zr3 * zi + zi3 * zr + ImPrim[j];
603 zr3 = Temp;
604 }
605
606 // f":
607 zr4 = zi4 = 0;
608 for (j = 0; j < c2; j++)
609 {
610 Temp = zr4 * zr - zi4 * zi + ReBis[j];
611 zi4 = zr4 * zi + zi4 * zr + ImBis[j];
612 zr4 = Temp;
613 }
614
615 // 2*f*f'
616
617 zr5 = 2 * (zr2 * zr3 - zi2 * zi3);
618 zi5 = 2 * (zr2 * zi3 + zi2 * zr3);
619
620 // 2f'^2-f*f"
621
622 zr6 = 2 * (zr3 * zr3 - zi3 * zi3) - (zr2 * zr4 - zi2 * zi4);
623 zi6 = 4 * zr3 * zi3 - (zr2 * zi4 + zr4 * zi2);
624
625 // R*2*f*f'/2f'^2-f*f"
626
627 Temp = 1.0 / (zr6 * zr6 + zi6 * zi6);
628 zr4 = (zr5 * zr6 + zi5 * zi6) * Temp;
629 zi4 = (zi5 * zr6 - zr5 * zi6) * Temp;
630
631 // R*2*f*f'/(2f'^2-f*f")
632 Temp = zr4 * RRe - zi4 * RIm;
633 zi4 = zr4 * RIm + zi4 * RRe;
634 zr4 = Temp;
635
636 zr -= zr4;
637 zi -= zi4;
638
639 Temp = Math.Sqrt(zr4 * zr4 + zi4 * zi4);
640 }
641 while ((Temp > Conv) && (Temp < Div) && (n++ < N));
642
643 if (Temp < Conv && n < N)
644 {
645 rgb[index++] = blues[n];
646 rgb[index++] = greens[n];
647 rgb[index++] = reds[n];
648 }
649 else
650 {
651 rgb[index++] = 0;
652 rgb[index++] = 0;
653 rgb[index++] = 0;
654 }
655
656 rgb[index++] = 255;
657 }
658 }
659
660 PixelInformation Pixels = new PixelInformationRaw(SKColorType.Bgra8888, rgb, Width, Height, Width << 2);
661 return new FractalGraph(Variables, Pixels, r0, i0, r1, i1, rDelta * 2, true, Node, FractalZoomScript, State);
662 }
663
667 public static FractalGraph CalcHalley(Variables Variables, double rCenter, double iCenter, double rDelta, Complex R,
668 ILambdaExpression f, ScriptNode _, SKColor[] Palette, int Width, int Height, ScriptNode Node,
669 FractalZoomScript FractalZoomScript, object State)
670 {
671 byte[] reds;
672 byte[] greens;
673 byte[] blues;
674 double RRe = R.Real;
675 double RIm = R.Imaginary;
676 double r0, i0, r1, i1;
677 double dr, di;
678 double r, i;
679 double aspect;
680 int x, y;
681 int n, N;
682 SKColor cl;
683
684 N = Palette.Length;
685 reds = new byte[N];
686 greens = new byte[N];
687 blues = new byte[N];
688
689 for (x = 0; x < N; x++)
690 {
691 cl = Palette[x];
692 reds[x] = cl.Red;
693 greens[x] = cl.Green;
694 blues[x] = cl.Blue;
695 }
696
697 Variables v = new Variables();
698 Variables.CopyTo(v);
699
700 string ParameterName;
701 if (!(f is IDifferentiable Differentiable) ||
702 !(Differentiable.Differentiate(ParameterName = Differentiable.DefaultVariableName, v) is ILambdaExpression fPrim))
703 {
704 throw new ScriptRuntimeException("Lambda expression not differentiable.", Node);
705 }
706
707 if (!(fPrim is IDifferentiable Differentiable2) ||
708 !(Differentiable2.Differentiate(ParameterName, v) is ILambdaExpression fBis))
709 {
710 throw new ScriptRuntimeException("Lambda expression not twice differentiable.", Node);
711 }
712
713 int size = Width * Height * 4;
714 double Conv = 1e-10;
715 double Div = 1e10;
716 byte[] rgb = new byte[size];
717
718 Complex[] Row;
719 Complex[] Row2;
720 Complex[] Row3;
721 Complex[] Row4;
722 int[] Offset;
723 IElement[] P = new IElement[1];
724 int j, c, x2;
725 IElement Obj, Obj2, Obj3;
726 double Mod;
727 Complex z, z2, z3;
728 Complex R2 = R * 2;
729
730 rDelta *= 0.5;
731 r0 = rCenter - rDelta;
732 r1 = rCenter + rDelta;
733
734 aspect = ((double)Width) / Height;
735
736 i0 = iCenter - rDelta / aspect;
737 i1 = iCenter + rDelta / aspect;
738
739 dr = (r1 - r0) / Width;
740 di = (i1 - i0) / Height;
741
742 for (y = 0, i = i0; y < Height; y++, i += di)
743 {
744 Row = new Complex[Width];
745 Offset = new int[Width];
746
747 c = Width;
748 for (x = 0, x2 = y * Width * 4, r = r0; x < Width; x++, r += dr, x2 += 4)
749 {
750 Row[x] = new Complex(r, i);
751 Offset[x] = x2;
752 }
753
754 n = 0;
755 while (n < N && c > 0)
756 {
757 n++;
758 P[0] = new ComplexVector(Row);
759 Obj = f.Evaluate(P, v);
760 Obj2 = fPrim.Evaluate(P, v);
761 Obj3 = fBis.Evaluate(P, v);
762 Row2 = Obj.AssociatedObjectValue as Complex[];
763 Row3 = Obj2.AssociatedObjectValue as Complex[];
764 Row4 = Obj3.AssociatedObjectValue as Complex[];
765
766 if (Row2 is null || Row3 is null || Row4 is null)
767 {
768 throw new ScriptRuntimeException("Lambda expression (and its first and second derivative) must be able to accept complex vectors, " +
769 "and return complex vectors of equal length. Type returned: " +
770 Obj.GetType().FullName + ", " + Obj2.GetType().FullName + " and " + Obj3.GetType().FullName,
771 Node);
772 }
773 else if (Row2.Length != c || Row3.Length != c)
774 {
775 throw new ScriptRuntimeException("Lambda expression (and its first and second derivative) must be able to accept complex vectors, " +
776 "and return complex vectors of equal length. Length returned: " +
777 Row2.Length.ToString() + ", " + Row3.Length.ToString() + " and " + Row4.Length.ToString() +
778 ". Expected: " + c.ToString(), Node);
779 }
780
781 for (x = x2 = 0; x < c; x++)
782 {
783 j = Offset[x];
784 z = Row2[x];
785 z2 = Row3[x];
786 z3 = Row4[x];
787
788 z = R2 * z * z2 / (2 * z2 * z2 - z * z3);
789 Row[x] -= z;
790
791 Mod = z.Magnitude;
792
793 if (Mod > Conv && Mod < Div)
794 {
795 if (x != x2)
796 Offset[x2] = j;
797
798 x2++;
799 }
800 else
801 {
802 if (n >= N)
803 {
804 rgb[j++] = 0;
805 rgb[j++] = 0;
806 rgb[j++] = 0;
807 }
808 else
809 {
810 rgb[j++] = blues[n];
811 rgb[j++] = greens[n];
812 rgb[j++] = reds[n];
813 }
814
815 rgb[j++] = 255;
816 }
817 }
818
819 if (x2 < x)
820 {
821 Array.Resize(ref Row, x2);
822 Array.Resize(ref Offset, x2);
823 c = x2;
824 }
825 }
826 }
827
828 PixelInformation Pixels = new PixelInformationRaw(SKColorType.Bgra8888, rgb, Width, Height, Width << 2);
829 return new FractalGraph(Variables, Pixels, r0, i0, r1, i1, rDelta * 2, true, Node, FractalZoomScript, State);
830 }
831
835 public override string FunctionName => nameof(HalleyFractal);
836 }
837}
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.HalleyFractal.HalleyFractal
HalleyFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode Coefficients, ScriptNode Palette, int Start, int Length, Expression Expression)
TODO
Definition: HalleyFractal.cs:69
Waher.Script.Fractals.ComplexFractals.HalleyFractal.HalleyFractal
HalleyFractal(ScriptNode z, ScriptNode dr, int Start, int Length, Expression Expression)
TODO
Definition: HalleyFractal.cs:100
Waher.Script.Fractals.ComplexFractals.HalleyFractal.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: HalleyFractal.cs:475
Waher.Script.Fractals.ComplexFractals.HalleyFractal.HalleyFractal
HalleyFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode Coefficients, ScriptNode Palette, ScriptNode DimX, int Start, int Length, Expression Expression)
TODO
Definition: HalleyFractal.cs:58
Waher.Script.Fractals.ComplexFractals.HalleyFractal.HalleyFractal
HalleyFractal(ScriptNode z, ScriptNode dr, ScriptNode R, int Start, int Length, Expression Expression)
TODO
Definition: HalleyFractal.cs:91
Waher.Script.Fractals.ComplexFractals.HalleyFractal.HalleyFractal
HalleyFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode Coefficients, ScriptNode Palette, ScriptNode DimX, ScriptNode DimY, int Start, int Length, Expression Expression)
TODO
Definition: HalleyFractal.cs:47
Waher.Script.Fractals.ComplexFractals.HalleyFractal.HalleyFractal
HalleyFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode Coefficients, int Start, int Length, Expression Expression)
TODO
Definition: HalleyFractal.cs:80
Waher.Script.Fractals.ComplexFractals.HalleyFractal.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)
Calculates a Halley Fractal
Definition: HalleyFractal.cs:315
Waher.Script.Fractals.ComplexFractals.HalleyFractal.Evaluate
override IElement Evaluate(IElement[] Arguments, Variables Variables)
TODO
Definition: HalleyFractal.cs:120
Waher.Script.Fractals.ComplexFractals.HalleyFractal.CalcHalley
static FractalGraph CalcHalley(Variables Variables, double rCenter, double iCenter, double rDelta, Complex R, ILambdaExpression f, ScriptNode _, SKColor[] Palette, int Width, int Height, ScriptNode Node, FractalZoomScript FractalZoomScript, object State)
TODO
Definition: HalleyFractal.cs:667
Waher.Script.Fractals.FractalGraph
Defines a clickable fractal graph in the complex plane.
Definition: FractalGraph.cs:22
Waher.Script.Fractals.FractalGraph.ToPalette
static SKColor[] ToPalette(ObjectVector Vector)
TODO
Definition: FractalGraph.cs:101
Waher.Script.Graphs.PixelInformation
Contains pixel information
Definition: PixelInformation.cs:9
Waher.Script.Graphs.PixelInformationRaw
Contains pixel information in a raw unencoded format.
Definition: PixelInformationRaw.cs:11
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