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NewtonBasinFractal.cs
1using System;
2using System.Collections.Generic;
3using System.Numerics;
4using System.Text;
5using SkiaSharp;
6using Waher.Script.Abstraction.Elements;
7using Waher.Script.Model;
8using Waher.Script.Exceptions;
9using Waher.Script.Graphs;
10using Waher.Script.Objects.VectorSpaces;
11
12namespace Waher.Script.Fractals.ComplexFractals
13{
38 public class NewtonBasinFractal : FunctionMultiVariate
39 {
43 public NewtonBasinFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode c, ScriptNode N,
44 ScriptNode DimX, ScriptNode DimY, int Start, int Length, Expression Expression)
45 : base(new ScriptNode[] { z, dr, R, c, N, DimX, DimY },
46 new ArgumentType[] { ArgumentType.Scalar, ArgumentType.Scalar, ArgumentType.Scalar,
47 ArgumentType.Normal, ArgumentType.Scalar, ArgumentType.Scalar, ArgumentType.Scalar},
48 Start, Length, Expression)
49 {
50 }
51
55 public NewtonBasinFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode c, ScriptNode N,
56 ScriptNode DimX, int Start, int Length, Expression Expression)
57 : base(new ScriptNode[] { z, dr, R, c, N, DimX },
58 new ArgumentType[] { ArgumentType.Scalar, ArgumentType.Scalar, ArgumentType.Scalar,
59 ArgumentType.Normal, ArgumentType.Scalar, ArgumentType.Scalar},
60 Start, Length, Expression)
61 {
62 }
63
67 public NewtonBasinFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode c, ScriptNode N,
68 int Start, int Length, Expression Expression)
69 : base(new ScriptNode[] { z, dr, R, c, N },
70 new ArgumentType[] { ArgumentType.Scalar, ArgumentType.Scalar, ArgumentType.Scalar,
71 ArgumentType.Normal, ArgumentType.Scalar },
72 Start, Length, Expression)
73 {
74 }
75
79 public NewtonBasinFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode c,
80 int Start, int Length, Expression Expression)
81 : base(new ScriptNode[] { z, dr, R, c },
82 new ArgumentType[] { ArgumentType.Scalar, ArgumentType.Scalar, ArgumentType.Scalar,
83 ArgumentType.Normal },
84 Start, Length, Expression)
85 {
86 }
87
91 public override string[] DefaultArgumentNames
92 {
93 get
94 {
95 return new string[] { "z", "dr", "R", "c", "N", "DimX", "DimY" };
96 }
97 }
98
102 public override IElement Evaluate(IElement[] Arguments, Variables Variables)
103 {
104 double[] Coefficients = null;
105 Complex[] CoefficientsZ = null;
106 ILambdaExpression f = null;
107 ScriptNode fDef = null;
108 double rc, ic;
109 double dr;
110 Complex R;
111 int N;
112 int dimx, dimy;
113 int c = Arguments.Length;
114 int i = 0;
115 object Obj;
116
117 Obj = Arguments[i++].AssociatedObjectValue;
118 if (Obj is Complex z)
119 {
120 rc = z.Real;
121 ic = z.Imaginary;
122 }
123 else
124 {
125 rc = Expression.ToDouble(Obj);
126 ic = Expression.ToDouble(Arguments[i++].AssociatedObjectValue);
127 }
128
129 if (i >= c)
130 throw new ScriptRuntimeException("Insufficient parameters in call to NewtonBasinFractal().", this);
131
132 dr = Expression.ToDouble(Arguments[i++].AssociatedObjectValue);
133
134 if (i < c && ((Obj = Arguments[i].AssociatedObjectValue) is double || Obj is Complex))
135 {
136 R = Expression.ToComplex(Obj);
137 i++;
138 }
139 else
140 {
141 R = Complex.One;
142
143 if (i < c && this.Arguments[i] is null)
144 i++;
145 }
146
147 if (i < c)
148 {
149 if (Arguments[i] is DoubleVector)
150 Coefficients = (double[])Arguments[i++].AssociatedObjectValue;
151 else if (Arguments[i] is ComplexVector)
152 CoefficientsZ = (Complex[])Arguments[i++].AssociatedObjectValue;
153 /*else if (Parameters[i] is RealPolynomial)
154 Coefficients = ((RealPolynomial)Arguments[i++].AssociatedObjectValue).Coefficients;
155 else if (Parameters[i] is ComplexPolynomial)
156 CoefficientsZ = ((ComplexPolynomial)Arguments[i++].AssociatedObjectValue).Coefficients;*/
157 else if (Arguments[i] is IVector)
158 {
159 IVector Vector = (IVector)Arguments[i++];
160 int j, d = Vector.Dimension;
161
162 CoefficientsZ = new Complex[d];
163 for (j = 0; j < d; j++)
164 CoefficientsZ[j] = Expression.ToComplex(Vector.GetElement(j).AssociatedObjectValue);
165 }
166 else if (Arguments[i].AssociatedObjectValue is ILambdaExpression)
167 {
168 f = (ILambdaExpression)Arguments[i];
169 if (f.NrArguments != 1)
170 throw new ScriptRuntimeException("Lambda expression in calls to NewtonBasinFractal() must be of one variable.", this);
171
172 fDef = this.Arguments[i++];
173 }
174 else
175 {
176 throw new ScriptRuntimeException("Parameter " + (i + 1).ToString() +
177 " in call to NewtonBasinFractal has to be a vector of numbers, containing coefficients " +
178 "of the polynomial to use. Now it was of type " + Arguments[i].GetType().FullName,
179 this);
180 }
181 }
182 else
183 throw new ScriptRuntimeException("Missing coefficients or lambda expression.", this);
184
185 if (i < c)
186 N = (int)Expression.ToDouble(Arguments[i++].AssociatedObjectValue);
187 else
188 N = 32;
189
190 if (i < c)
191 dimx = (int)Expression.ToDouble(Arguments[i++].AssociatedObjectValue);
192 else
193 dimx = 320;
194
195 if (i < c)
196 dimy = (int)Expression.ToDouble(Arguments[i++].AssociatedObjectValue);
197 else
198 dimy = 200;
199
200 if (i < c)
201 {
202 throw new ScriptRuntimeException("Parameter mismatch in call to NewtonBasinFractal(r,c,dr,Coefficients[,Palette][,dimx[,dimy]]).",
203 this);
204 }
205
206 if (dimx <= 0 || dimx > 5000 || dimy <= 0 || dimy > 5000)
207 throw new ScriptRuntimeException("Image size must be within 1x1 to 5000x5000", this);
208
209 if (!(f is null))
210 {
211 return CalcNewton(rc, ic, dr, R, f, fDef, Variables, N, dimx, dimy, this, this.FractalZoomScript,
212 new object[] { dimx, dimy, N, R, fDef });
213 }
214 else if (!(CoefficientsZ is null))
215 {
216 return CalcNewton(Variables, rc, ic, dr, R, CoefficientsZ, N, dimx, dimy, this, this.FractalZoomScript,
217 new object[] { dimx, dimy, N, R, CoefficientsZ });
218 }
219 else
220 {
221 return CalcNewton(Variables, rc, ic, dr, R, Coefficients, N, dimx, dimy, this, this.FractalZoomScript,
222 new object[] { dimx, dimy, N, R, Coefficients });
223 }
224 }
225
226 private string FractalZoomScript(double r, double i, double Size, object State)
227 {
228 object[] Parameters = (object[])State;
229 int DimX = (int)Parameters[0];
230 int DimY = (int)Parameters[1];
231 int N = (int)Parameters[2];
232 Complex R = (Complex)Parameters[3];
233 double[] Coefficients = Parameters[4] as double[];
234
235 StringBuilder sb = new StringBuilder();
236
237 sb.Append("NewtonBasinFractal((");
238 sb.Append(Expression.ToString(r));
239 sb.Append(',');
240 sb.Append(Expression.ToString(i));
241 sb.Append("),");
242 sb.Append(Expression.ToString(Size / 4));
243 sb.Append(',');
244 sb.Append(Expression.ToString(R));
245 sb.Append(',');
246
247 if (Parameters[4] is ScriptNode fDef)
248 sb.Append(fDef.SubExpression);
249 else if (Parameters[4] is Complex[] CoefficientsZ)
250 sb.Append(Expression.ToString(CoefficientsZ));
251 else
252 sb.Append(Expression.ToString(Coefficients));
253
254 sb.Append(',');
255 sb.Append(N.ToString());
256 sb.Append(',');
257 sb.Append(DimX.ToString());
258 sb.Append(',');
259 sb.Append(DimY.ToString());
260 sb.Append(')');
261
262 return sb.ToString();
263 }
264
268 public static FractalGraph CalcNewton(Variables Variables, double rCenter, double iCenter, double rDelta, Complex R,
269 double[] Coefficients, int N, int Width, int Height, ScriptNode Node, FractalZoomScript FractalZoomScript, object State)
270 {
271 double RRe = R.Real;
272 double RIm = R.Imaginary;
273 List<double> AttractorsR = new List<double>();
274 List<double> AttractorsI = new List<double>();
275 List<int> AttractorColors = new List<int>();
276 double[] AttractorsR2 = new double[0];
277 double[] AttractorsI2 = new double[0];
278 int[] AttractorsColors2 = new int[0];
279 double r0, i0, r1, i1;
280 double dr, di;
281 double r, i;
282 double zr, zi, zr2, zi2, zr3, zi3, zr4, zi4;
283 double aspect;
284 double Temp;
285 int x, y, b, c = 0, d;
286 int n;
287 int index;
288 int Degree = Coefficients.Length - 1;
289
290 if (Degree < 2)
291 {
292 Array.Resize(ref Coefficients, 3);
293 while (Degree < 2)
294 Coefficients[++Degree] = 0;
295 }
296
297 double[] Prim = new double[Degree];
298 for (x = 1; x <= Degree; x++)
299 Prim[x - 1] = x * Coefficients[x];
300
301 Array.Reverse(Prim);
302 Coefficients = (double[])Coefficients.Clone();
303 Array.Reverse(Coefficients);
304
305 int size = Width * Height * 4;
306 double Conv = 1e-10;
307 double Div = 1e10;
308 double Conv2 = Conv * 2;
309 byte[] rgb = new byte[size];
310
311 rDelta *= 0.5;
312 r0 = rCenter - rDelta;
313 r1 = rCenter + rDelta;
314
315 aspect = ((double)Width) / Height;
316
317 i0 = iCenter - rDelta / aspect;
318 i1 = iCenter + rDelta / aspect;
319
320 dr = (r1 - r0) / Width;
321 di = (i1 - i0) / Height;
322
323 for (y = 0, i = i0, index = 0; y < Height; y++, i += di)
324 {
325 for (x = 0, r = r0; x < Width; x++, r += dr)
326 {
327 zr = r;
328 zi = i;
329
330 n = 0;
331 do
332 {
333 // f:
334 zr2 = zi2 = 0;
335 foreach (double C in Coefficients)
336 {
337 Temp = zr2 * zr - zi2 * zi + C;
338 zi2 = zr2 * zi + zi2 * zr;
339 zr2 = Temp;
340 }
341
342 // f':
343 zr3 = zi3 = 0;
344 foreach (double C in Prim)
345 {
346 Temp = zr3 * zr - zi3 * zi + C;
347 zi3 = zr3 * zi + zi3 * zr;
348 zr3 = Temp;
349 }
350
351 // f/f':
352
353 Temp = 1.0 / (zr3 * zr3 + zi3 * zi3);
354 zr4 = (zr2 * zr3 + zi2 * zi3) * Temp;
355 zi4 = (zi2 * zr3 - zr2 * zi3) * Temp;
356
357 // R*f/f'
358 Temp = zr4 * RRe - zi4 * RIm;
359 zi4 = zr4 * RIm + zi4 * RRe;
360 zr4 = Temp;
361
362 zr -= zr4;
363 zi -= zi4;
364
365 Temp = Math.Sqrt(zr4 * zr4 + zi4 * zi4);
366 }
367 while ((Temp > Conv) && (Temp < Div) && (n++ < N));
368
369 if (Temp < Conv && n < N)
370 {
371 for (b = 0; b < c; b++)
372 {
373 if (Math.Abs(AttractorsR2[b] - zr) < Conv2 &&
374 Math.Abs(AttractorsI2[b] - zi) < Conv2)
375 {
376 break;
377 }
378 }
379
380 if (b == c)
381 {
382 AttractorsR.Add(zr);
383 AttractorsI.Add(zi);
384
385 int p1 = ~((b % 6) + 1);
386 int p2 = ((b / 6) % 7);
387
388 int Red = (p1 & 1) != 0 ? 255 : 0;
389 int Green = (p1 & 2) != 0 ? 255 : 0;
390 int Blue = (p1 & 4) != 0 ? 255 : 0;
391
392 if ((p2 & 1) != 0)
393 Red >>= 1;
394
395 if ((p2 & 2) != 0)
396 Green >>= 1;
397
398 if ((p2 & 4) != 0)
399 Blue >>= 1;
400
401 Blue <<= 8;
402 Blue |= Green;
403 Blue <<= 8;
404 Blue |= Red;
405
406 AttractorColors.Add(Blue);
407
408 AttractorsR2 = AttractorsR.ToArray();
409 AttractorsI2 = AttractorsI.ToArray();
410 AttractorsColors2 = AttractorColors.ToArray();
411
412 c++;
413 }
414
415 b = AttractorColors[b];
416
417 d = (byte)b;
418 rgb[index++] = (byte)((d * (N - n + 1)) / N);
419 b >>= 8;
420 d = (byte)b;
421 rgb[index++] = (byte)((d * (N - n + 1)) / N);
422 b >>= 8;
423 d = (byte)b;
424 rgb[index++] = (byte)((d * (N - n + 1)) / N);
425 }
426 else
427 {
428 rgb[index++] = 0;
429 rgb[index++] = 0;
430 rgb[index++] = 0;
431 }
432
433 rgb[index++] = 255;
434 }
435 }
436
437 PixelInformation Pixels = new PixelInformationRaw(SKColorType.Bgra8888, rgb, Width, Height, Width << 2);
438 return new FractalGraph(Variables, Pixels, r0, i0, r1, i1, rDelta * 2, true, Node, FractalZoomScript, State);
439 }
440
444 public static FractalGraph CalcNewton(Variables Variables, double rCenter, double iCenter, double rDelta, Complex R,
445 Complex[] Coefficients, int N, int Width, int Height, ScriptNode Node, FractalZoomScript FractalZoomScript, object State)
446 {
447 double RRe = R.Real;
448 double RIm = R.Imaginary;
449 List<double> AttractorsR = new List<double>();
450 List<double> AttractorsI = new List<double>();
451 List<int> AttractorColors = new List<int>();
452 double[] AttractorsR2 = new double[0];
453 double[] AttractorsI2 = new double[0];
454 int[] AttractorsColors2 = new int[0];
455 double r0, i0, r1, i1;
456 double dr, di;
457 double r, i;
458 double zr, zi, zr2, zi2, zr3, zi3, zr4, zi4;
459 double aspect;
460 double Temp;
461 int x, y, b, c = 0, d;
462 int n;
463 int index;
464 int Degree = Coefficients.Length - 1;
465
466 if (Degree < 2)
467 {
468 Array.Resize(ref Coefficients, 3);
469 while (Degree < 2)
470 Coefficients[++Degree] = Complex.Zero;
471 }
472
473 Complex[] Prim = new Complex[Degree];
474 for (x = 1; x <= Degree; x++)
475 Prim[x - 1] = x * Coefficients[x];
476
477 Array.Reverse(Prim);
478 Coefficients = (Complex[])Coefficients.Clone();
479 Array.Reverse(Coefficients);
480
481 int j, e = Prim.Length;
482 double[] ReC = new double[e + 1];
483 double[] ImC = new double[e + 1];
484 double[] RePrim = new double[e];
485 double[] ImPrim = new double[e];
486 Complex z;
487
488 for (j = 0; j < e; j++)
489 {
490 z = Coefficients[j];
491 ReC[j] = z.Real;
492 ImC[j] = z.Imaginary;
493
494 z = Prim[j];
495 RePrim[j] = z.Real;
496 ImPrim[j] = z.Imaginary;
497 }
498
499 z = Coefficients[j];
500 ReC[j] = z.Real;
501 ImC[j] = z.Imaginary;
502
503 int size = Width * Height * 4;
504 double Conv = 1e-10;
505 double Div = 1e10;
506 double Conv2 = Conv * 2;
507 byte[] rgb = new byte[size];
508
509 rDelta *= 0.5;
510 r0 = rCenter - rDelta;
511 r1 = rCenter + rDelta;
512
513 aspect = ((double)Width) / Height;
514
515 i0 = iCenter - rDelta / aspect;
516 i1 = iCenter + rDelta / aspect;
517
518 dr = (r1 - r0) / Width;
519 di = (i1 - i0) / Height;
520
521 for (y = 0, i = i0, index = 0; y < Height; y++, i += di)
522 {
523 for (x = 0, r = r0; x < Width; x++, r += dr)
524 {
525 zr = r;
526 zi = i;
527
528 n = 0;
529 do
530 {
531 // f:
532 zr2 = zi2 = 0;
533 for (j = 0; j <= e; j++)
534 {
535 Temp = zr2 * zr - zi2 * zi + ReC[j];
536 zi2 = zr2 * zi + zi2 * zr + ImC[j];
537 zr2 = Temp;
538 }
539
540 // f':
541 zr3 = zi3 = 0;
542 for (j = 0; j < e; j++)
543 {
544 Temp = zr3 * zr - zi3 * zi + RePrim[j];
545 zi3 = zr3 * zi + zi3 * zr + ImPrim[j];
546 zr3 = Temp;
547 }
548
549 // f/f':
550
551 Temp = 1.0 / (zr3 * zr3 + zi3 * zi3);
552 zr4 = (zr2 * zr3 + zi2 * zi3) * Temp;
553 zi4 = (zi2 * zr3 - zr2 * zi3) * Temp;
554
555 // R*f/f'
556 Temp = zr4 * RRe - zi4 * RIm;
557 zi4 = zr4 * RIm + zi4 * RRe;
558 zr4 = Temp;
559
560 zr -= zr4;
561 zi -= zi4;
562
563 Temp = Math.Sqrt(zr4 * zr4 + zi4 * zi4);
564 }
565 while ((Temp > Conv) && (Temp < Div) && (n++ < N));
566
567 if (Temp < Conv && n < N)
568 {
569 for (b = 0; b < c; b++)
570 {
571 if (Math.Abs(AttractorsR2[b] - zr) < Conv2 &&
572 Math.Abs(AttractorsI2[b] - zi) < Conv2)
573 {
574 break;
575 }
576 }
577
578 if (b == c)
579 {
580 AttractorsR.Add(zr);
581 AttractorsI.Add(zi);
582
583 int p1 = ~((b % 6) + 1);
584 int p2 = ((b / 6) % 7);
585
586 int Red = (p1 & 1) != 0 ? 255 : 0;
587 int Green = (p1 & 2) != 0 ? 255 : 0;
588 int Blue = (p1 & 4) != 0 ? 255 : 0;
589
590 if ((p2 & 1) != 0)
591 Red >>= 1;
592
593 if ((p2 & 2) != 0)
594 Green >>= 1;
595
596 if ((p2 & 4) != 0)
597 Blue >>= 1;
598
599 Blue <<= 8;
600 Blue |= Green;
601 Blue <<= 8;
602 Blue |= Red;
603
604 AttractorColors.Add(Blue);
605
606 AttractorsR2 = AttractorsR.ToArray();
607 AttractorsI2 = AttractorsI.ToArray();
608 AttractorsColors2 = AttractorColors.ToArray();
609
610 c++;
611 }
612
613 b = AttractorColors[b];
614
615 d = (byte)b;
616 rgb[index++] = (byte)((d * (N - n + 1)) / N);
617 b >>= 8;
618 d = (byte)b;
619 rgb[index++] = (byte)((d * (N - n + 1)) / N);
620 b >>= 8;
621 d = (byte)b;
622 rgb[index++] = (byte)((d * (N - n + 1)) / N);
623 }
624 else
625 {
626 rgb[index++] = 0;
627 rgb[index++] = 0;
628 rgb[index++] = 0;
629 }
630
631 rgb[index++] = 255;
632 }
633 }
634
635 PixelInformation Pixels = new PixelInformationRaw(SKColorType.Bgra8888, rgb, Width, Height, Width << 2);
636 return new FractalGraph(Variables, Pixels, r0, i0, r1, i1, rDelta * 2, true, Node, FractalZoomScript, State);
637 }
638
642 public static FractalGraph CalcNewton(double rCenter, double iCenter, double rDelta, Complex R,
643 ILambdaExpression f, ScriptNode _, Variables Variables, int N, int Width, int Height,
644 ScriptNode Node, FractalZoomScript FractalZoomScript, object State)
645 {
646 double RRe = R.Real;
647 double RIm = R.Imaginary;
648 List<double> AttractorsR = new List<double>();
649 List<double> AttractorsI = new List<double>();
650 List<int> AttractorColors = new List<int>();
651 double[] AttractorsR2 = new double[0];
652 double[] AttractorsI2 = new double[0];
653 int[] AttractorsColors2 = new int[0];
654 double r0, i0, r1, i1;
655 double dr, di;
656 double r, i;
657 double zr, zi;
658 double aspect;
659 int x, y, b, c, d;
660 int NrAttractors = 0;
661 int n;
662 int index;
663
664 Variables v = new Variables();
665 Variables.CopyTo(v);
666
667 if (!(f is IDifferentiable Differentiable) ||
668 !(Differentiable.Differentiate(Differentiable.DefaultVariableName, v) is ILambdaExpression fPrim))
669 {
670 throw new ScriptRuntimeException("Lambda expression not differentiable.", Node);
671 }
672
673 int size = Width * Height * 4;
674 double Conv = 1e-10;
675 double Div = 1e10;
676 double Conv2 = Conv * 2;
677 byte[] rgb = new byte[size];
678
679 Complex[] Row;
680 Complex[] Row2;
681 Complex[] Row3;
682 int[] Offset;
683 IElement[] P = new IElement[1];
684 int j, x2;
685 IElement Obj, Obj2;
686 double Mod;
687 Complex z;
688
689 rDelta *= 0.5;
690 r0 = rCenter - rDelta;
691 r1 = rCenter + rDelta;
692
693 aspect = ((double)Width) / Height;
694
695 i0 = iCenter - rDelta / aspect;
696 i1 = iCenter + rDelta / aspect;
697
698 dr = (r1 - r0) / Width;
699 di = (i1 - i0) / Height;
700
701 for (y = 0, i = i0, index = 0; y < Height; y++, i += di)
702 {
703 Row = new Complex[Width];
704 Offset = new int[Width];
705
706 c = Width;
707 for (x = 0, x2 = y * Width * 4, r = r0; x < Width; x++, r += dr, x2 += 4)
708 {
709 Row[x] = new Complex(r, i);
710 Offset[x] = x2;
711 }
712
713 n = 0;
714 while (n < N && c > 0)
715 {
716 n++;
717 P[0] = new ComplexVector(Row);
718 Obj = f.Evaluate(P, v);
719 Obj2 = fPrim.Evaluate(P, v);
720 Row2 = Obj.AssociatedObjectValue as Complex[];
721 Row3 = Obj2.AssociatedObjectValue as Complex[];
722
723 if (Row2 is null || Row3 is null)
724 {
725 throw new ScriptRuntimeException("Lambda expression (and its first derivative) must be able to accept complex vectors, " +
726 "and return complex vectors of equal length. Type returned: " +
727 Obj.GetType().FullName + " and " + Obj2.GetType().FullName, Node);
728 }
729 else if (Row2.Length != c || Row3.Length != c)
730 {
731 throw new ScriptRuntimeException("Lambda expression (and its first derivative) must be able to accept complex vectors, " +
732 "and return complex vectors of equal length. Length returned: " +
733 Row2.Length.ToString() + " and " + Row3.Length.ToString() +
734 ". Expected: " + c.ToString(), Node);
735 }
736
737 for (x = x2 = 0; x < c; x++)
738 {
739 j = Offset[x];
740 z = R * Row2[x] / Row3[x];
741 Row[x] -= z;
742
743 Mod = z.Magnitude;
744
745 if (Mod > Conv && Mod < Div)
746 {
747 if (x != x2)
748 Offset[x2] = j;
749
750 x2++;
751 }
752 else
753 {
754 if (n >= N)
755 {
756 rgb[j++] = 0;
757 rgb[j++] = 0;
758 rgb[j++] = 0;
759 }
760 else
761 {
762 zr = z.Real;
763 zi = z.Imaginary;
764
765 for (b = 0; b < NrAttractors; b++)
766 {
767 if (Math.Abs(AttractorsR2[b] - zr) < Conv2 &&
768 Math.Abs(AttractorsI2[b] - zi) < Conv2)
769 {
770 break;
771 }
772 }
773
774 if (b == NrAttractors)
775 {
776 AttractorsR.Add(zr);
777 AttractorsI.Add(zi);
778
779 int p1 = ~((b % 6) + 1);
780 int p2 = ((b / 6) % 7);
781
782 int Red = (p1 & 1) != 0 ? 255 : 0;
783 int Green = (p1 & 2) != 0 ? 255 : 0;
784 int Blue = (p1 & 4) != 0 ? 255 : 0;
785
786 if ((p2 & 1) != 0)
787 Red >>= 1;
788
789 if ((p2 & 2) != 0)
790 Green >>= 1;
791
792 if ((p2 & 4) != 0)
793 Blue >>= 1;
794
795 Blue <<= 8;
796 Blue |= Green;
797 Blue <<= 8;
798 Blue |= Red;
799
800 AttractorColors.Add(Blue);
801
802 AttractorsR2 = AttractorsR.ToArray();
803 AttractorsI2 = AttractorsI.ToArray();
804 AttractorsColors2 = AttractorColors.ToArray();
805
806 NrAttractors++;
807 }
808
809 b = AttractorColors[b];
810
811 d = (byte)b;
812 rgb[index++] = (byte)((d * (N - n + 1)) / N);
813 b >>= 8;
814 d = (byte)b;
815 rgb[index++] = (byte)((d * (N - n + 1)) / N);
816 b >>= 8;
817 d = (byte)b;
818 rgb[index++] = (byte)((d * (N - n + 1)) / N);
819 }
820
821 rgb[j++] = 255;
822 }
823 }
824
825 if (x2 < x)
826 {
827 Array.Resize(ref Row, x2);
828 Array.Resize(ref Offset, x2);
829 c = x2;
830 }
831 }
832
833 }
834
835 PixelInformation Pixels = new PixelInformationRaw(SKColorType.Bgra8888, rgb, Width, Height, Width << 2);
836 return new FractalGraph(Variables, Pixels, r0, i0, r1, i1, rDelta * 2, true, Node, FractalZoomScript, State);
837 }
838
842 public override string FunctionName => nameof(NewtonBasinFractal);
843 }
844}
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.NewtonBasinFractal.NewtonBasinFractal
NewtonBasinFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode c, ScriptNode N, ScriptNode DimX, ScriptNode DimY, int Start, int Length, Expression Expression)
TODO
Definition: NewtonBasinFractal.cs:43
Waher.Script.Fractals.ComplexFractals.NewtonBasinFractal.NewtonBasinFractal
NewtonBasinFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode c, int Start, int Length, Expression Expression)
TODO
Definition: NewtonBasinFractal.cs:79
Waher.Script.Fractals.ComplexFractals.NewtonBasinFractal.CalcNewton
static FractalGraph CalcNewton(Variables Variables, double rCenter, double iCenter, double rDelta, Complex R, double[] Coefficients, int N, int Width, int Height, ScriptNode Node, FractalZoomScript FractalZoomScript, object State)
TODO
Definition: NewtonBasinFractal.cs:268
Waher.Script.Fractals.ComplexFractals.NewtonBasinFractal.NewtonBasinFractal
NewtonBasinFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode c, ScriptNode N, ScriptNode DimX, int Start, int Length, Expression Expression)
TODO
Definition: NewtonBasinFractal.cs:55
Waher.Script.Fractals.ComplexFractals.NewtonBasinFractal.Evaluate
override IElement Evaluate(IElement[] Arguments, Variables Variables)
TODO
Definition: NewtonBasinFractal.cs:102
Waher.Script.Fractals.ComplexFractals.NewtonBasinFractal.CalcNewton
static FractalGraph CalcNewton(double rCenter, double iCenter, double rDelta, Complex R, ILambdaExpression f, ScriptNode _, Variables Variables, int N, int Width, int Height, ScriptNode Node, FractalZoomScript FractalZoomScript, object State)
TODO
Definition: NewtonBasinFractal.cs:642
Waher.Script.Fractals.ComplexFractals.NewtonBasinFractal.CalcNewton
static FractalGraph CalcNewton(Variables Variables, double rCenter, double iCenter, double rDelta, Complex R, Complex[] Coefficients, int N, int Width, int Height, ScriptNode Node, FractalZoomScript FractalZoomScript, object State)
TODO
Definition: NewtonBasinFractal.cs:444
Waher.Script.Fractals.ComplexFractals.NewtonBasinFractal.NewtonBasinFractal
NewtonBasinFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode c, ScriptNode N, int Start, int Length, Expression Expression)
TODO
Definition: NewtonBasinFractal.cs:67
Waher.Script.Fractals.FractalGraph
Defines a clickable fractal graph in the complex plane.
Definition: FractalGraph.cs:22
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