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NewtonFractal.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{
46 public class NewtonFractal : FunctionMultiVariate
47 {
51 public NewtonFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode c, ScriptNode Palette,
52 ScriptNode DimX, ScriptNode DimY, int Start, int Length, Expression Expression)
53 : base(new ScriptNode[] { z, dr, R, c, Palette, DimX, DimY },
54 new ArgumentType[] { ArgumentType.Scalar, ArgumentType.Scalar, ArgumentType.Scalar,
55 ArgumentType.Normal, ArgumentType.Vector, ArgumentType.Scalar, ArgumentType.Scalar},
56 Start, Length, Expression)
57 {
58 }
59
63 public NewtonFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode c, ScriptNode Palette,
64 ScriptNode DimX, int Start, int Length, Expression Expression)
65 : base(new ScriptNode[] { z, dr, R, c, Palette, DimX },
66 new ArgumentType[] { ArgumentType.Scalar, ArgumentType.Scalar, ArgumentType.Scalar,
67 ArgumentType.Normal, ArgumentType.Vector, ArgumentType.Scalar},
68 Start, Length, Expression)
69 {
70 }
71
75 public NewtonFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode c, ScriptNode Palette,
76 int Start, int Length, Expression Expression)
77 : base(new ScriptNode[] { z, dr, R, c, Palette },
78 new ArgumentType[] { ArgumentType.Scalar, ArgumentType.Scalar, ArgumentType.Scalar,
79 ArgumentType.Normal, ArgumentType.Vector },
80 Start, Length, Expression)
81 {
82 }
83
87 public NewtonFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode c,
88 int Start, int Length, Expression Expression)
89 : base(new ScriptNode[] { z, dr, R, c },
90 new ArgumentType[] { ArgumentType.Scalar, ArgumentType.Scalar, ArgumentType.Scalar,
91 ArgumentType.Normal },
92 Start, Length, Expression)
93 {
94 }
95
99 public override string[] DefaultArgumentNames
100 {
101 get
102 {
103 return new string[] { "z", "dr", "R", "c", "Palette", "DimX", "DimY" };
104 }
105 }
106
110 public override IElement Evaluate(IElement[] Arguments, Variables Variables)
111 {
112 string ColorExpression = null;
113 SKColor[] Palette;
114 double[] Coefficients = null;
115 Complex[] CoefficientsZ = null;
116 ILambdaExpression f = null;
117 ScriptNode fDef = null;
118 double rc, ic;
119 double dr;
120 Complex R;
121 int dimx, dimy;
122 int c = Arguments.Length;
123 int i = 0;
124 object Obj;
125
126 Obj = Arguments[i++].AssociatedObjectValue;
127 if (Obj is Complex z)
128 {
129 rc = z.Real;
130 ic = z.Imaginary;
131 }
132 else
133 {
134 rc = Expression.ToDouble(Obj);
135 ic = Expression.ToDouble(Arguments[i++].AssociatedObjectValue);
136 }
137
138 if (i >= c)
139 throw new ScriptRuntimeException("Insufficient parameters in call to NewtonFractal().", this);
140
141 dr = Expression.ToDouble(Arguments[i++].AssociatedObjectValue);
142
143 if (i < c && ((Obj = Arguments[i].AssociatedObjectValue) is double || Obj is Complex))
144 {
145 R = Expression.ToComplex(Obj);
146 i++;
147 }
148 else
149 {
150 R = Complex.One;
151
152 if (i < c && this.Arguments[i] is null)
153 i++;
154 }
155
156 if (i < c)
157 {
158 if (Arguments[i] is DoubleVector)
159 Coefficients = (double[])Arguments[i++].AssociatedObjectValue;
160 else if (Arguments[i] is ComplexVector)
161 CoefficientsZ = (Complex[])Arguments[i++].AssociatedObjectValue;
162 /*else if (Parameters[i] is RealPolynomial)
163 Coefficients = ((RealPolynomial)Arguments[i++].AssociatedObjectValue).Coefficients;
164 else if (Parameters[i] is ComplexPolynomial)
165 CoefficientsZ = ((ComplexPolynomial)Arguments[i++].AssociatedObjectValue).Coefficients;*/
166 else if (Arguments[i] is IVector)
167 {
168 IVector Vector = (IVector)Arguments[i++];
169 int j, d = Vector.Dimension;
170
171 CoefficientsZ = new Complex[d];
172 for (j = 0; j < d; j++)
173 CoefficientsZ[j] = Expression.ToComplex(Vector.GetElement(j).AssociatedObjectValue);
174 }
175 else if (Arguments[i].AssociatedObjectValue is ILambdaExpression)
176 {
177 f = (ILambdaExpression)Arguments[i];
178 if (f.NrArguments != 1)
179 throw new ScriptRuntimeException("Lambda expression in calls to NewtonFractal() must be of one variable.", this);
180
181 fDef = this.Arguments[i++];
182 }
183 else
184 {
185 throw new ScriptRuntimeException("Parameter " + (i + 1).ToString() +
186 " in call to NewtonFractal has to be a vector of numbers, containing coefficients " +
187 "of the polynomial to use. Now it was of type " + Arguments[i].GetType().FullName,
188 this);
189 }
190 }
191 else
192 throw new ScriptRuntimeException("Missing coefficients or lambda expression.", this);
193
194 if (i < c && !(this.Arguments[i] is null) && Arguments[i] is ObjectVector)
195 {
196 ColorExpression = this.Arguments[i].SubExpression;
197 Palette = FractalGraph.ToPalette((ObjectVector)Arguments[i++]);
198 }
199 else
200 {
201 Palette = ColorModels.RandomLinearAnalogousHSL.CreatePalette(128, 4, out int Seed, this, Variables);
202 ColorExpression = "RandomLinearAnalogousHSL(128,4," + Seed.ToString() + ")";
203
204 if (i < c && this.Arguments[i] is null)
205 i++;
206 }
207
208 if (i < c)
209 dimx = (int)Expression.ToDouble(Arguments[i++].AssociatedObjectValue);
210 else
211 dimx = 320;
212
213 if (i < c)
214 dimy = (int)Expression.ToDouble(Arguments[i++].AssociatedObjectValue);
215 else
216 dimy = 200;
217
218 if (i < c)
219 {
220 throw new ScriptRuntimeException("Parameter mismatch in call to NewtonFractal(r,c,dr,Coefficients[,Palette][,dimx[,dimy]]).",
221 this);
222 }
223
224 if (dimx <= 0 || dimx > 5000 || dimy <= 0 || dimy > 5000)
225 throw new ScriptRuntimeException("Image size must be within 1x1 to 5000x5000", this);
226
227 if (!(f is null))
228 {
229 return CalcNewton(rc, ic, dr, R, f, fDef, Variables, Palette, dimx, dimy,
230 this, this.FractalZoomScript, new object[] { Palette, dimx, dimy, R, fDef, ColorExpression });
231 }
232 else if (!(CoefficientsZ is null))
233 {
234 return CalcNewton(Variables, rc, ic, dr, R, CoefficientsZ, Palette, dimx, dimy,
235 this, this.FractalZoomScript, new object[] { Palette, dimx, dimy, R, CoefficientsZ, ColorExpression });
236 }
237 else
238 {
239 return CalcNewton(Variables, rc, ic, dr, R, Coefficients, Palette, dimx, dimy,
240 this, this.FractalZoomScript, new object[] { Palette, dimx, dimy, R, Coefficients, ColorExpression });
241 }
242 }
243
244 private string FractalZoomScript(double r, double i, double Size, object State)
245 {
246 object[] Parameters = (object[])State;
247 int DimX = (int)Parameters[1];
248 int DimY = (int)Parameters[2];
249 Complex R = (Complex)Parameters[3];
250 double[] Coefficients = Parameters[4] as double[];
251 string ColorExpression = (string)Parameters[5];
252
253 StringBuilder sb = new StringBuilder();
254
255 sb.Append("NewtonFractal((");
256 sb.Append(Expression.ToString(r));
257 sb.Append(',');
258 sb.Append(Expression.ToString(i));
259 sb.Append("),");
260 sb.Append(Expression.ToString(Size / 4));
261 sb.Append(',');
262 sb.Append(Expression.ToString(R));
263 sb.Append(',');
264
265 if (Parameters[4] is ScriptNode fDef)
266 sb.Append(fDef.SubExpression);
267 else if (Parameters[4] is Complex[] CoefficientsZ)
268 sb.Append(Expression.ToString(CoefficientsZ));
269 else
270 sb.Append(Expression.ToString(Coefficients));
271
272 if (!string.IsNullOrEmpty(ColorExpression))
273 {
274 sb.Append(',');
275 sb.Append(ColorExpression);
276 }
277
278 sb.Append(',');
279 sb.Append(DimX.ToString());
280 sb.Append(',');
281 sb.Append(DimY.ToString());
282 sb.Append(')');
283
284 return sb.ToString();
285 }
286
290 public static FractalGraph CalcNewton(Variables Variables, double rCenter, double iCenter, double rDelta, Complex R,
291 double[] Coefficients, SKColor[] Palette, int Width, int Height, ScriptNode Node, FractalZoomScript FractalZoomScript,
292 object State)
293 {
294 byte[] reds;
295 byte[] greens;
296 byte[] blues;
297 double r0, i0, r1, i1;
298 double dr, di;
299 double r, i;
300 double zr, zi, zr2, zi2, zr3, zi3, zr4, zi4;
301 double RRe = R.Real;
302 double RIm = R.Imaginary;
303 double aspect;
304 double Temp;
305 int x, y;
306 int n, N;
307 int index;
308 int Degree = Coefficients.Length - 1;
309 SKColor cl;
310
311 N = Palette.Length;
312 reds = new byte[N];
313 greens = new byte[N];
314 blues = new byte[N];
315
316 for (x = 0; x < N; x++)
317 {
318 cl = Palette[x];
319 reds[x] = cl.Red;
320 greens[x] = cl.Green;
321 blues[x] = cl.Blue;
322 }
323
324 if (Degree < 2)
325 {
326 Array.Resize(ref Coefficients, 3);
327 while (Degree < 2)
328 Coefficients[++Degree] = 0;
329 }
330
331 double[] Prim = new double[Degree];
332 for (x = 1; x <= Degree; x++)
333 Prim[x - 1] = x * Coefficients[x];
334
335 Array.Reverse(Prim);
336 Coefficients = (double[])Coefficients.Clone();
337 Array.Reverse(Coefficients);
338
339 int size = Width * Height * 4;
340 double Conv = 1e-10;
341 double Div = 1e10;
342 byte[] rgb = new byte[size];
343
344 rDelta *= 0.5;
345 r0 = rCenter - rDelta;
346 r1 = rCenter + rDelta;
347
348 aspect = ((double)Width) / Height;
349
350 i0 = iCenter - rDelta / aspect;
351 i1 = iCenter + rDelta / aspect;
352
353 dr = (r1 - r0) / Width;
354 di = (i1 - i0) / Height;
355
356 for (y = 0, i = i0, index = 0; y < Height; y++, i += di)
357 {
358 for (x = 0, r = r0; x < Width; x++, r += dr)
359 {
360 zr = r;
361 zi = i;
362
363 n = 0;
364 do
365 {
366 // f:
367 zr2 = zi2 = 0;
368 foreach (double C in Coefficients)
369 {
370 Temp = zr2 * zr - zi2 * zi + C;
371 zi2 = zr2 * zi + zi2 * zr;
372 zr2 = Temp;
373 }
374
375 // f':
376 zr3 = zi3 = 0;
377 foreach (double C in Prim)
378 {
379 Temp = zr3 * zr - zi3 * zi + C;
380 zi3 = zr3 * zi + zi3 * zr;
381 zr3 = Temp;
382 }
383
384 // f/f':
385
386 Temp = 1.0 / (zr3 * zr3 + zi3 * zi3);
387 zr4 = (zr2 * zr3 + zi2 * zi3) * Temp;
388 zi4 = (zi2 * zr3 - zr2 * zi3) * Temp;
389
390 // R*f/f'
391 Temp = zr4 * RRe - zi4 * RIm;
392 zi4 = zr4 * RIm + zi4 * RRe;
393 zr4 = Temp;
394
395 zr -= zr4;
396 zi -= zi4;
397
398 Temp = Math.Sqrt(zr4 * zr4 + zi4 * zi4);
399 }
400 while ((Temp > Conv) && (Temp < Div) && (n++ < N));
401
402 if (Temp < Conv && n < N)
403 {
404 rgb[index++] = blues[n];
405 rgb[index++] = greens[n];
406 rgb[index++] = reds[n];
407 }
408 else
409 {
410 rgb[index++] = 0;
411 rgb[index++] = 0;
412 rgb[index++] = 0;
413 }
414
415 rgb[index++] = 255;
416 }
417 }
418
419 PixelInformation Pixels = new PixelInformationRaw(SKColorType.Bgra8888, rgb, Width, Height, Width << 2);
420 return new FractalGraph(Variables, Pixels, r0, i0, r1, i1, rDelta * 2, true, Node, FractalZoomScript, State);
421 }
422
426 public static FractalGraph CalcNewton(Variables Variables, double rCenter, double iCenter, double rDelta, Complex R,
427 Complex[] Coefficients, SKColor[] Palette, int Width, int Height, ScriptNode Node, FractalZoomScript FractalZoomScript,
428 object State)
429 {
430 byte[] reds;
431 byte[] greens;
432 byte[] blues;
433 double RRe = R.Real;
434 double RIm = R.Imaginary;
435 double r0, i0, r1, i1;
436 double dr, di;
437 double r, i;
438 double zr, zi, zr2, zi2, zr3, zi3, zr4, zi4;
439 double aspect;
440 double Temp;
441 int x, y;
442 int n, N;
443 int index;
444 int Degree = Coefficients.Length - 1;
445 SKColor cl;
446
447 N = Palette.Length;
448 reds = new byte[N];
449 greens = new byte[N];
450 blues = new byte[N];
451
452 for (x = 0; x < N; x++)
453 {
454 cl = Palette[x];
455 reds[x] = cl.Red;
456 greens[x] = cl.Green;
457 blues[x] = cl.Blue;
458 }
459
460 if (Degree < 2)
461 {
462 Array.Resize(ref Coefficients, 3);
463 while (Degree < 2)
464 Coefficients[++Degree] = Complex.Zero;
465 }
466
467 Complex[] Prim = new Complex[Degree];
468 for (x = 1; x <= Degree; x++)
469 Prim[x - 1] = x * Coefficients[x];
470
471 Array.Reverse(Prim);
472 Coefficients = (Complex[])Coefficients.Clone();
473 Array.Reverse(Coefficients);
474
475 int j, c = Prim.Length;
476 double[] ReC = new double[c + 1];
477 double[] ImC = new double[c + 1];
478 double[] RePrim = new double[c];
479 double[] ImPrim = new double[c];
480 Complex z;
481
482 for (j = 0; j < c; j++)
483 {
484 z = Coefficients[j];
485 ReC[j] = z.Real;
486 ImC[j] = z.Imaginary;
487
488 z = Prim[j];
489 RePrim[j] = z.Real;
490 ImPrim[j] = z.Imaginary;
491 }
492
493 z = Coefficients[j];
494 ReC[j] = z.Real;
495 ImC[j] = z.Imaginary;
496
497 int size = Width * Height * 4;
498 double Conv = 1e-10;
499 double Div = 1e10;
500 byte[] rgb = new byte[size];
501
502 rDelta *= 0.5;
503 r0 = rCenter - rDelta;
504 r1 = rCenter + rDelta;
505
506 aspect = ((double)Width) / Height;
507
508 i0 = iCenter - rDelta / aspect;
509 i1 = iCenter + rDelta / aspect;
510
511 dr = (r1 - r0) / Width;
512 di = (i1 - i0) / Height;
513
514 for (y = 0, i = i0, index = 0; y < Height; y++, i += di)
515 {
516 for (x = 0, r = r0; x < Width; x++, r += dr)
517 {
518 zr = r;
519 zi = i;
520
521 n = 0;
522 do
523 {
524 // f:
525 zr2 = zi2 = 0;
526 for (j = 0; j <= c; j++)
527 {
528 Temp = zr2 * zr - zi2 * zi + ReC[j];
529 zi2 = zr2 * zi + zi2 * zr + ImC[j];
530 zr2 = Temp;
531 }
532
533 // f':
534 zr3 = zi3 = 0;
535 for (j = 0; j < c; j++)
536 {
537 Temp = zr3 * zr - zi3 * zi + RePrim[j];
538 zi3 = zr3 * zi + zi3 * zr + ImPrim[j];
539 zr3 = Temp;
540 }
541
542 // f/f':
543
544 Temp = 1.0 / (zr3 * zr3 + zi3 * zi3);
545 zr4 = (zr2 * zr3 + zi2 * zi3) * Temp;
546 zi4 = (zi2 * zr3 - zr2 * zi3) * Temp;
547
548 // R*f/f'
549 Temp = zr4 * RRe - zi4 * RIm;
550 zi4 = zr4 * RIm + zi4 * RRe;
551 zr4 = Temp;
552
553 zr -= zr4;
554 zi -= zi4;
555
556 Temp = Math.Sqrt(zr4 * zr4 + zi4 * zi4);
557 }
558 while ((Temp > Conv) && (Temp < Div) && (n++ < N));
559
560 if (Temp < Conv && n < N)
561 {
562 rgb[index++] = blues[n];
563 rgb[index++] = greens[n];
564 rgb[index++] = reds[n];
565 }
566 else
567 {
568 rgb[index++] = 0;
569 rgb[index++] = 0;
570 rgb[index++] = 0;
571 }
572
573 rgb[index++] = 255;
574 }
575 }
576
577 PixelInformation Pixels = new PixelInformationRaw(SKColorType.Bgra8888, rgb, Width, Height, Width << 2);
578 return new FractalGraph(Variables, Pixels, r0, i0, r1, i1, rDelta * 2, true, Node, FractalZoomScript, State);
579 }
580
584 public static FractalGraph CalcNewton(double rCenter, double iCenter, double rDelta, Complex R,
585 ILambdaExpression f, ScriptNode _, Variables Variables, SKColor[] Palette, int Width, int Height,
586 ScriptNode Node, FractalZoomScript FractalZoomScript, object State)
587 {
588 byte[] reds;
589 byte[] greens;
590 byte[] blues;
591 double RRe = R.Real;
592 double RIm = R.Imaginary;
593 double r0, i0, r1, i1;
594 double dr, di;
595 double r, i;
596 double aspect;
597 int x, y;
598 int n, N;
599 SKColor cl;
600 Complex z;
601
602 N = Palette.Length;
603 reds = new byte[N];
604 greens = new byte[N];
605 blues = new byte[N];
606
607 for (x = 0; x < N; x++)
608 {
609 cl = Palette[x];
610 reds[x] = cl.Red;
611 greens[x] = cl.Green;
612 blues[x] = cl.Blue;
613 }
614
615 Variables v = new Variables();
616 Variables.CopyTo(v);
617
618 if (!(f is IDifferentiable Differentiable) ||
619 !(Differentiable.Differentiate(Differentiable.DefaultVariableName, v) is ILambdaExpression fPrim))
620 {
621 throw new ScriptRuntimeException("Lambda expression not differentiable.", Node);
622 }
623
624 int size = Width * Height * 4;
625 double Conv = 1e-10;
626 double Div = 1e10;
627 byte[] rgb = new byte[size];
628
629 Complex[] Row;
630 Complex[] Row2;
631 Complex[] Row3;
632 int[] Offset;
633 IElement[] P = new IElement[1];
634 int j, c, x2;
635 IElement Obj, Obj2;
636 double Mod;
637
638 rDelta *= 0.5;
639 r0 = rCenter - rDelta;
640 r1 = rCenter + rDelta;
641
642 aspect = ((double)Width) / Height;
643
644 i0 = iCenter - rDelta / aspect;
645 i1 = iCenter + rDelta / aspect;
646
647 dr = (r1 - r0) / Width;
648 di = (i1 - i0) / Height;
649
650 for (y = 0, i = i0; y < Height; y++, i += di)
651 {
652 Row = new Complex[Width];
653 Offset = new int[Width];
654
655 c = Width;
656 for (x = 0, x2 = y * Width * 4, r = r0; x < Width; x++, r += dr, x2 += 4)
657 {
658 Row[x] = new Complex(r, i);
659 Offset[x] = x2;
660 }
661
662 n = 0;
663 while (n < N && c > 0)
664 {
665 n++;
666 P[0] = new ComplexVector(Row);
667 Obj = f.Evaluate(P, v);
668 Obj2 = fPrim.Evaluate(P, v);
669 Row2 = Obj.AssociatedObjectValue as Complex[];
670 Row3 = Obj2.AssociatedObjectValue as Complex[];
671
672 if (Row2 is null || Row3 is null)
673 {
674 throw new ScriptRuntimeException("Lambda expression (and its first derivative) must be able to accept complex vectors, " +
675 "and return complex vectors of equal length. Type returned: " +
676 Obj.GetType().FullName + " and " + Obj2.GetType().FullName, Node);
677 }
678 else if (Row2.Length != c || Row3.Length != c)
679 {
680 throw new ScriptRuntimeException("Lambda expression (and its first derivative) must be able to accept complex vectors, " +
681 "and return complex vectors of equal length. Length returned: " +
682 Row2.Length.ToString() + " and " + Row3.Length.ToString() +
683 ". Expected: " + c.ToString(), Node);
684 }
685
686 for (x = x2 = 0; x < c; x++)
687 {
688 j = Offset[x];
689 z = R * Row2[x] / Row3[x];
690 Row[x] -= z;
691
692 Mod = z.Magnitude;
693
694 if (Mod > Conv && Mod < Div)
695 {
696 if (x != x2)
697 Offset[x2] = j;
698
699 x2++;
700 }
701 else
702 {
703 if (n >= N)
704 {
705 rgb[j++] = 0;
706 rgb[j++] = 0;
707 rgb[j++] = 0;
708 }
709 else
710 {
711 rgb[j++] = blues[n];
712 rgb[j++] = greens[n];
713 rgb[j++] = reds[n];
714 }
715
716 rgb[j++] = 255;
717 }
718 }
719
720 if (x2 < x)
721 {
722 Array.Resize(ref Row, x2);
723 Array.Resize(ref Offset, x2);
724 c = x2;
725 }
726 }
727 }
728
729 PixelInformation Pixels = new PixelInformationRaw(SKColorType.Bgra8888, rgb, Width, Height, Width << 2);
730 return new FractalGraph(Variables, Pixels, r0, i0, r1, i1, rDelta * 2, true, Node, FractalZoomScript, State);
731 }
732
736 public override string FunctionName => nameof(NewtonFractal);
737 }
738}
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.NewtonFractal.CalcNewton
static FractalGraph CalcNewton(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: NewtonFractal.cs:426
Waher.Script.Fractals.ComplexFractals.NewtonFractal.Evaluate
override IElement Evaluate(IElement[] Arguments, Variables Variables)
TODO
Definition: NewtonFractal.cs:110
Waher.Script.Fractals.ComplexFractals.NewtonFractal.NewtonFractal
NewtonFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode c, ScriptNode Palette, ScriptNode DimX, int Start, int Length, Expression Expression)
TODO
Definition: NewtonFractal.cs:63
Waher.Script.Fractals.ComplexFractals.NewtonFractal.CalcNewton
static FractalGraph CalcNewton(double rCenter, double iCenter, double rDelta, Complex R, ILambdaExpression f, ScriptNode _, Variables Variables, SKColor[] Palette, int Width, int Height, ScriptNode Node, FractalZoomScript FractalZoomScript, object State)
TODO
Definition: NewtonFractal.cs:584
Waher.Script.Fractals.ComplexFractals.NewtonFractal.NewtonFractal
NewtonFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode c, ScriptNode Palette, int Start, int Length, Expression Expression)
TODO
Definition: NewtonFractal.cs:75
Waher.Script.Fractals.ComplexFractals.NewtonFractal.NewtonFractal
NewtonFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode c, int Start, int Length, Expression Expression)
TODO
Definition: NewtonFractal.cs:87
Waher.Script.Fractals.ComplexFractals.NewtonFractal.NewtonFractal
NewtonFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode c, ScriptNode Palette, ScriptNode DimX, ScriptNode DimY, int Start, int Length, Expression Expression)
TODO
Definition: NewtonFractal.cs:51
Waher.Script.Fractals.ComplexFractals.NewtonFractal.CalcNewton
static FractalGraph CalcNewton(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: NewtonFractal.cs:290
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