• January 16, 2021, 01:57:09 PM

### Author Topic:  Lagrangian Descriptors Fragment code  (Read 500 times)

0 Members and 1 Guest are viewing this topic.

#### 3DickUlus

• Posts: 1975
##### Lagrangian Descriptors Fragment code
« on: June 23, 2020, 01:01:57 AM »
Based on Unveiling Fractal Structure with Lagrangian Descriptors
Code: [Select]
/* partial pnorm   input: z, c, p   output ppn*/float ppnorm( vec2 z, vec2 c, float p){ vec3 s0,s1; // for 2 points on the Riemann sphere float d; // denominator // map from complex plane to riemann sphere // z d = z.x*z.x + z.y*z.y + 1.0; s0 = vec3(2.0*z,(d-2.0))/d; // c d = c.x*c.x + c.y*c.y + 1.0; s1 = vec3(2.0*c,(d-2.0))/d; // sum vec3 ss = pow(abs(s1 - s0),vec3(p)); return ss.x+ss.y+ss.z;}// DLD = Discret Lagrangian Descriptiorfloat lagrangian( vec2 z, vec2 c, float p ){ int i; // number of iteration float d = 0.0; // DLD = sum for (i=0; i<Iterations; ++i){ d += ppnorm(z, c, p); // sum z z = cMul(z,z) +c; // complex iteration if (cAbs(z) > 1e19 ) break; // exterior : upper limit of float type } d /= float(i); // averaging not summation return d;}

Modified and optimized for GLSL ( disclaimer: it may or may not be mathematically correct but it looks nice and it's fun to play with )

« Last Edit: June 23, 2020, 04:34:32 AM by 3DickUlus »

• Fractal Frogurt
• Posts: 433
##### Re: Lagrangian Descriptors Fragment code
« Reply #1 on: June 23, 2020, 03:19:13 PM »

cool.
Rays and equipotential curves of exterior and interior are visualised. Is it possible to modify parameters to remove additional curves ? ( not rays or equipotentials)

I like Juli set. It is for c = -1.065000000000000 ? = -1.05204872
Can you post all parameters ? All are in the frag (:-))
Can you put it to commons? ( I can do it if you agree) because it so cool image

« Last Edit: June 23, 2020, 04:00:06 PM by Adam Majewski, Reason: c = »

• Fractal Frogurt
• Posts: 433
##### Re: Lagrangian Descriptors Fragment code
« Reply #2 on: June 23, 2020, 06:04:18 PM »
Here is my code. It shuld give similar Julia image in gray
For interior it gives similar result, but exterior not
How can I improve it?

Code: [Select]
/*  Adam Majewski  adammaj1 aaattt o2 dot pl  // o like oxygen not 0 like zero           ==============================================      Structure of a program or how to analyze the program       ============== Image X ========================    DrawImageOfX -> DrawPointOfX -> ComputeColorOfX     first 2 functions are identical for every X  check only last function =  ComputeColorOfX  which computes color of one pixel !         ==========================================    ---------------------------------  indent d.c   default is gnu style   -------------------  c console progam   export  OMP_DISPLAY_ENV="TRUE"   gcc d.c -lm -Wall -march=native -fopenmp  time ./a.out > b.txt  gcc d.c -lm -Wall -march=native -fopenmp  time ./a.out  time ./a.out >i.txt  time ./a.out >e.txt    =======================  # gnuplot "i.plt"set terminal svg enhanced background rgb 'white'set xlabel "re(z)"set ylabel "DLD"set title "Relation between z and DLD in the interior of Julia set for c = -1"set output "interior.svg"plot "i.txt" with lines  ----------------------  d0 - db  = 5.0000000000000000 - 4.5389870050569598 = 0.4610129949430402 allways free memory (deallocate )  to avoid memory leaks Numerical approximation of Julia set for fc(z)= z^2 + c parameter c = ( -1.0000000000000000 ; 0.0000000000000000 ) Image Width = 4.000000 in world coordinatePixelWidth = 0.004004 Maximal number of iterations = iterMax = 1000 ratio of image  = 1.000000 ; it should be 1.000 ...gcc version: 7.5.0    */#include <stdio.h>#include <stdlib.h> // malloc#include <string.h> // strcat#include <math.h> // M_PI; needs -lm also#include <complex.h>#include <omp.h> // OpenMP// https://sourceforge.net/p/predef/wiki/Standards/#if defined(__STDC__)# define PREDEF_STANDARD_C_1989# if defined(__STDC_VERSION__)#  if (__STDC_VERSION__ >= 199409L)#   define PREDEF_STANDARD_C_1994#  endif#  if (__STDC_VERSION__ >= 199901L)#   define PREDEF_STANDARD_C_1999#  endif# endif#endif/* --------------------------------- global variables and consts ------------------------------------------------------------ */// virtual 2D array and integer ( screen) coordinate// Indexes of array starts from 0 not 1 //unsigned int ix, iy; // varstatic unsigned int ixMin = 0; // Indexes of array starts from 0 not 1static unsigned int ixMax; //static unsigned int iWidth; // horizontal dimension of arraystatic unsigned int iyMin = 0; // Indexes of array starts from 0 not 1static unsigned int iyMax; //static unsigned int iHeight = 5000; //  // The size of array has to be a positive constant integer static unsigned int iSize; // = iWidth*iHeight; // memmory 1D array unsigned char *data;//unsigned char *edge;//unsigned char *edge2;// unsigned int i; // var = index of 1D array//static unsigned int iMin = 0; // Indexes of array starts from 0 not 1static unsigned int iMax; // = i2Dsize-1  = // The size of array has to be a positive constant integer // unsigned int i1Dsize ; // = i2Dsize  = (iMax -iMin + 1) =  ;  1D array with the same size as 2D arraystatic const double ZxMin = -1.8; //-0.05;static const double ZxMax =  1.8; //0.75;static const double ZyMin = -1.8; //-0.1;static const double ZyMax =  1.8; //0.7;static double PixelWidth; // =(ZxMax-ZxMin)/ixMax;static double PixelHeight; // =(ZyMax-ZyMin)/iyMax;static double ratio;// complex numbers of parametr plane //https://fractalforums.org/code-snippets-fragments/74/lagrangian-descriptors-fragment-code/3612/msg22426#msg22426double complex c = -1.05204872; // parameter of function fc(z)=z^2 + c// attracting period 2 cycle double complex z21 = 0.049822582293598;double complex z22 = -1.049822582293598;double complex z1a  = -0.641073494565534; // alfacomplex double z1b = 1.641073494565534; // betadouble complex zb = 0.203208556149733  +0.377005347593583*I; // point on the boubndary of main componnetint ARe = 60;int ERe = 16;double ER ;//= 1e60;double AR ;//= 1e-16; // bigger values do not works// DLDconst int N = 20; // fixed number : maximal number of iterationsdouble p  = 0.01444322;  //// DLD colorsdouble me = 1.0;double mi = 10.0;double d21; // = lagrangian(z21, c, N, p);double d22; //  = lagrangian(z22, c, N, p);double db;// = lagrangian(z1a, c, N, p); double dd;// = d1a-d21;/* colors = shades of gray from 0 to 255 */unsigned char iColorOfExterior = 250;unsigned char iColorOfInterior = 200;unsigned char iColorOfBoundary = 0;/* ------------------------------------------ functions -------------------------------------------------------------*///------------------complex numbers -----------------------------------------------------// from screen to world coordinate ; linear mapping// uses global consdouble GiveZx ( int ix){  return (ZxMin + ix * PixelWidth);}// uses globaal consdouble GiveZy (int iy) {  return (ZyMax - iy * PixelHeight);} // reverse y axiscomplex double GiveZ( int ix, int iy){  double Zx = GiveZx(ix);  double Zy = GiveZy(iy);   return Zx + Zy*I; }// ****************** DYNAMICS = trap tests ( target sets) ****************************/* -----------  array functions = drawing -------------- *//* gives position of 2D point (ix,iy) in 1D array  ; uses also global variable iWidth */unsigned int Give_i (unsigned int ix, unsigned int iy){  return ix + iy * iWidth;}// ***********************************************************************************************// ********************** edge detection usung Sobel filter ***************************************// ***************************************************************************************************// from Source to Destinationint ComputeBoundaries(unsigned char S[], unsigned char D[]){   unsigned int iX,iY; /* indices of 2D virtual array (image) = integer coordinate */  unsigned int i; /* index of 1D array  */  /* sobel filter */  unsigned char G, Gh, Gv;   // boundaries are in D  array ( global var )   // clear D array  memset(D, iColorOfExterior, iSize*sizeof(*D)); // for heap-allocated arrays, where N is the number of elements = FillArrayWithColor(D , iColorOfExterior);   // printf(" find boundaries in S array using  Sobel filter\n");   #pragma omp parallel for schedule(dynamic) private(i,iY,iX,Gv,Gh,G) shared(iyMax,ixMax)  for(iY=1;iY<iyMax-1;++iY){     for(iX=1;iX<ixMax-1;++iX){       Gv= S[Give_i(iX-1,iY+1)] + 2*S[Give_i(iX,iY+1)] + S[Give_i(iX-1,iY+1)] - S[Give_i(iX-1,iY-1)] - 2*S[Give_i(iX-1,iY)] - S[Give_i(iX+1,iY-1)];      Gh= S[Give_i(iX+1,iY+1)] + 2*S[Give_i(iX+1,iY)] + S[Give_i(iX-1,iY-1)] - S[Give_i(iX+1,iY-1)] - 2*S[Give_i(iX-1,iY)] - S[Give_i(iX-1,iY-1)];      G = sqrt(Gh*Gh + Gv*Gv);      i= Give_i(iX,iY); /* compute index of 1D array from indices of 2D array */      if (G==0) {D[i]=255;} /* background */      else {D[i]=0;}  /* boundary */    }  }       return 0;}// copy from Source to Destinationint CopyBoundaries(unsigned char S[],  unsigned char D[]){   unsigned int iX,iY; /* indices of 2D virtual array (image) = integer coordinate */  unsigned int i; /* index of 1D array  */    //printf("copy boundaries from S array to D array \n");  for(iY=1;iY<iyMax-1;++iY)    for(iX=1;iX<ixMax-1;++iX)      {i= Give_i(iX,iY); if (S[i]==0) D[i]=0;}     return 0;}// ***************************************************************************************************************************// ************************** DLD/J*****************************************// ****************************************************************************************************************************/* partial pnorm    input: z , zn = f(z), p   output ppn      */double ppnorm( complex double z, complex double zn, double p){ double s[2][3]; // array for 2 points on the Riemann sphere int j; double d; // denominator double x; double y; double ds; double ppn = 0.0; // map from complex plane to riemann sphere // z x = creal(z); y = cimag(z); d = x*x + y*y + 1.0; s[0][0] = (2.0*x)/d; s[0][1] = (2.0*y)/d;  s[0][2] = (d-2.0)/d; // (x^2 + y^2 - 1)/d // zn x = creal(zn); y = cimag(zn); d = x*x + y*y + 1.0; s[1][0] = (2.0*x)/d; s[1][1] = (2.0*y)/d;  s[1][2] = (d-2.0)/d; // (x^2 + y^2 - 1)/d // sum for (j=0; j <3; ++j){ ds = fabs(s[1][j] - s[0][j]); //  normal:  neither zero, subnormal, infinite, nor NaN //if (fpclassify (ds) !=FP_INFINITE) //if (isnormal(ds)) // it is solved by if (cabs(z) > 1e60 ) break; procedure in parent function ppn += pow(ds,p); // |ds|^p // else {ppn = 10000.0; printf("ds = infty\t");} // } return ppn; }// DLD = Discret Lagrangian Descriptiordouble lagrangian( complex double z0, complex double c, int iMax, double p ){ int i; // number of iteration double d = 0.0; // DLD = sum double ppn; // partial pnorm complex double z = z0; complex double zn; // next z for (i=0; i<iMax; ++i){ zn = z*z +c; // complex iteration ppn = ppnorm(z, zn, p); d += ppn; // sum // z = zn; //if (! isnormal(d)) { return 0.0; } // not works if (cabs(z) > ER ) break; // exterior : big values produces NAN error in ppnorm computing if (cabs(z - z21) < AR || cabs(z -z22)< AR) { // interior //return FP_ZERO; d = -d; break; } } if (d<0.0) {// interior // d(z1a) - d(z21) = -0.0804163521959989 d = - d; d = (db - d) /dd ; // normalize, see test_interior //if (d>1.0) {printf("d int > 1.0\n");d = d - (int)d;} // fractional part} } else { d =  d/((double)i); // averaging not summation d = d*me;} // exterior return d; }unsigned char ComputeColorOfDLD(complex double z){    //double cabsz;  int iColor;  double d;    d = lagrangian(z,c, N,p);  //if ( d==FP_ZERO)   // {iColor = 255;}  // else   iColor = (int)(d*255)  % 255; // nMax or lower walues in denominator      return (unsigned char) iColor;}// plots raster point (ix,iy) int DrawPointOfDLD (unsigned char A[], int ix, int iy){  int i; /* index of 1D array */  unsigned char iColor;  complex double z;  i = Give_i (ix, iy); /* compute index of 1D array from indices of 2D array */  z = GiveZ(ix,iy);  iColor = ComputeColorOfDLD(z);  A[i] = iColor ; // interior    return 0;}// fill array // uses global var :  ...// scanning complex plane int DrawImagerOfDLD (unsigned char A[]){  unsigned int ix, iy; // pixel coordinate   //printf("compute image \n");  // for all pixels of image #pragma omp parallel for schedule(dynamic) private(ix,iy) shared(A, ixMax , iyMax)  for (iy = iyMin; iy <= iyMax; ++iy){    printf (" %d from %d \r", iy, iyMax); //info     for (ix = ixMin; ix <= ixMax; ++ix)      DrawPointOfDLD(A, ix, iy); //    }  return 0;}// test how values changes to tune color // from z21 to zbint test_interior(){ complex double z = z21; complex double dz = cabs(z21 - zb)/15.0; double r = cabs(zb); printf("# re(z) \t d\n"); // gnuplot while (creal(z) < r){ // from z21 to z1a double d = lagrangian(z, c, N, p); //int iColor = ComputeColorOfDLD(z); // printf(" z = %.16f d = %.16f color = %d \n",creal(z), d, iColor); printf(" %.16f %.16f \n",creal(z), d); // gnuplot z += dz; } // d21 = lagrangian(z21, c, N, p); db = lagrangian(zb, c, N, p); d22 = lagrangian(z22, c, N, p); dd = db - d21; printf("d(z21) = %.16f \n",d21); printf("d(z22) = %.16f \n",d22); printf("d(zb) = %.16f \n",db); printf("d(zb) - d(z21) = %.16f\n",dd);; return 0;}   // test how values changes to tune color int test_exterior(){ complex double z; complex double z0 = 1.62; complex double z1 = 3.0; complex double dz = 0.001; z = z0; printf("# z d\n"); // gnuplot while (creal(z) < creal(z1)){ double d = lagrangian(z, c, N, p); //int iColor = ComputeColorOfDLD(z); // printf(" z = %.16f d = %.16f color = %d \n",creal(z), d, iColor); printf(" %.16f %.16f \n",creal(z), d); // gnuplot z += dz; } // double d0 = lagrangian(z0, c, N, p); double d1 = lagrangian(z1, c, N, p); double dd = d0 - d1; printf("d0 - d1  = %.16f - %.16f = %.16f\n",d0, d1, dd); return 0;}  // *******************************************************************************************// ********************************** save A array to pgm file ****************************// *********************************************************************************************int SaveArray2PGMFile( unsigned char A[], int a, int b, int c, int d,char* comment ){    FILE * fp;  const unsigned int MaxColorComponentValue=255; /* color component is coded from 0 to 255 ;  it is 8 bit color file */  char name [100]; /* name of file */  snprintf(name, sizeof name, "%d_%d_%d_%d", a,b,c,d); /*  */  char *filename =strcat(name,".pgm");  char long_comment[200];  sprintf (long_comment, "%s\tER = %e\tAR =%e", comment, ER, AR);           // save image array to the pgm file   fp= fopen(filename,"wb"); // create new file,give it a name and open it in binary mode   fprintf(fp,"P5\n # %s\n %u %u\n %u\n", long_comment, iWidth, iHeight, MaxColorComponentValue);  // write header to the file  fwrite(A,iSize,1,fp);  // write array with image data bytes to the file in one step   fclose(fp);     // info   printf("File %s saved ", filename);  if (long_comment == NULL || strlen(long_comment) ==0)      printf("\n");  else printf (". Comment = %s \n", long_comment);   return 0;}int PrintCInfo(){ printf("gcc version: %d.%d.%d\n",__GNUC__,__GNUC_MINOR__,__GNUC_PATCHLEVEL__); // https://stackoverflow.com/questions/20389193/how-do-i-check-my-gcc-c-compiler-version-for-my-eclipse  // OpenMP version is displayed in the console : export  OMP_DISPLAY_ENV="TRUE"  printf("__STDC__ = %d\n",  __STDC__ );  printf("__STDC_VERSION__ = %ld\n", __STDC_VERSION__ );  printf("c dialect = "); switch(__STDC_VERSION__) { // the format YYYYMM case 199409L  : printf("C94\n"); break; case 199901L  : printf("C99\n"); break; case 201112L  : printf("C11\n"); break; case 201710L  : printf("C18\n"); break; //default : /* Optional */    } return 0;}int PrintProgramInfo(){    // display info messages  printf ("Numerical approximation of Julia set for fc(z)= z^2 + c \n");  //printf ("iPeriodParent = %d \n", iPeriodParent);  //printf ("iPeriodOfChild  = %d \n", iPeriodChild);  printf ("parameter c = ( %.16f ; %.16f ) \n", creal(c), cimag(c));    printf ("Image Width = %f in world coordinate\n", ZxMax - ZxMin);  printf ("PixelWidth = %f \n", PixelWidth);     // image corners in world coordinate  // center and radius  // center and zoom  // GradientRepetition  printf ("Maximal number of iterations = iterMax = %d \n", N);  printf ("ratio of image  = %f ; it should be 1.000 ...\n", ratio);  //          return 0;}// *****************************************************************************//;;;;;;;;;;;;;;;;;;;;;;  setup ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;// **************************************************************************************int setup (){  printf ("setup start\n");             /* 2D array ranges */    iWidth = iHeight;  iSize = iWidth * iHeight; // size = number of points in array   // iy  iyMax = iHeight - 1; // Indexes of array starts from 0 not 1 so the highest elements of an array is = array_name[size-1].  //ix  ixMax = iWidth - 1;  /* 1D array ranges */  // i1Dsize = i2Dsize; // 1D array with the same size as 2D array  iMax = iSize - 1; // Indexes of array starts from 0 not 1 so the highest elements of an array is = array_name[size-1].  /* Pixel sizes */  PixelWidth = (ZxMax - ZxMin) / ixMax; //  ixMax = (iWidth-1)  step between pixels in world coordinate   PixelHeight = (ZyMax - ZyMin) / iyMax;  ratio = ((ZxMax - ZxMin) / (ZyMax - ZyMin)) / ((double) iWidth / (double) iHeight); // it should be 1.000 ...    ER = pow(10,ARe);   AR = pow(10,-ERe);         /* create dynamic 1D arrays for colors ( shades of gray ) */  data = malloc (iSize * sizeof (unsigned char));        if (data == NULL  ){    fprintf (stderr, " Could not allocate memory");    return 1;  }          test_interior();       printf (" end of setup \n");   return 0;} // ;;;;;;;;;;;;;;;;;;;;;;;;; end of the setup ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;int end(){  printf (" allways free memory (deallocate )  to avoid memory leaks \n"); // https://en.wikipedia.org/wiki/C_dynamic_memory_allocation  free (data);      PrintProgramInfo();  PrintCInfo();  return 0;}// ********************************************************************************************************************/* -----------------------------------------  main   -------------------------------------------------------------*/// ********************************************************************************************************************int main () {  setup ();        DrawImagerOfDLD(data);  SaveArray2PGMFile (data, iWidth,N,ERe, ARe,"DLD/J , name = iWidth_N_ER_AR");  //test_exterior();    end();  return 0;}
« Last Edit: June 23, 2020, 08:32:38 PM by Adam Majewski »

#### 3DickUlus

• Posts: 1975
##### Re: Lagrangian Descriptors Fragment code
« Reply #3 on: June 24, 2020, 01:54:24 AM »
the only real difference is that I'm passing z and c while your (original) code was passing Zn and Zn+1, that brings out the different pattern for interior... really interesting how the same function looks completely different inside vs outside for Julia.

GLSL types management allows for considerable streamlining, for instance, you use arrays in C while GLSL uses 2 vec3s

and the loop...

Code: [Select]
// sum for (j=0; j <3; ++j){ ds = fabs(s[1][j] - s[0][j]); ppn += pow(ds,p); // |ds|^p } is replaced with...
Code: [Select]
 vec3 ss = pow(abs(s1 - s0),vec3(p)); return ss.x+ss.y+ss.z;
this works because the pow() and abs() functions are general, they perform the same action on each corresponding part x,y and z and the GPU does them all at once.

another optimization in GLSL turns this...
Code: [Select]
 s[0][0] = (2.0*x)/d; s[0][1] = (2.0*y)/d; s[0][2] = (d-2.0)/d; // (x^2 + y^2 - 1)/dinto this...
Code: [Select]
s0 = vec3(2.0*z,(d-2.0))/d;
if you want to use GLSL like var types and math for C program then install the GLM library and #include glm.h

I also set the upper and lower limits to 1e+19 and 1e-19 respectively, I think that will remove the bands from the exterior.
« Last Edit: June 25, 2020, 02:35:56 AM by 3DickUlus »

#### Sabine62

• Moderator
• Posts: 1076
##### Re: Lagrangian Descriptors Fragment code
« Reply #4 on: June 24, 2020, 04:51:27 PM »
Thanks you for sharing, Dick!
To thine own self be true

• Fractal Frogurt
• Posts: 433
##### Re: Lagrangian Descriptors Fragment code
« Reply #5 on: June 24, 2020, 09:38:13 PM »
I have modified the algorithm.

First I divide pixels into interior and exterior using 2 tests:
Code: [Select]
for (i=0; i<IterMax; ++i){  z = z*z +c; // complex iteration  if (cabs(z) > 2.0 ) { return iColorOfExterior ; }// exterior : big values produces NAN error in ppnorm computing   if (cabs(z - z21) < AR || cabs(z -z22)< AR)  {  return iColorOfInterior ; }}  return iColorOfUnknown; // tune parameters to have 0 such points

Then I compute dld using different valus for exterior and interior

https://commons.wikimedia.org/wiki/File:Julia_set_c_%3D_-1.05204872_DLD.png

I put the frag code to wikibooks
Is it OK ?
https://en.wikibooks.org/wiki/Fractals/Iterations_in_the_complex_plane/Discrete_Lagrangian_Descriptors

Compare interior with :

« Last Edit: June 24, 2020, 10:21:18 PM by Adam Majewski, Reason: https://commons.wikimedia.org/w/index.php?title=File%3AQuadratic_Julia_set_with_Internal_binary_decomposition_for_internal_ray_0.ogv »

#### 3DickUlus

• Posts: 1975
##### Re: Lagrangian Descriptors Fragment code
« Reply #6 on: June 24, 2020, 11:47:22 PM »
I didn't explicitly give permission to post the fragment code but its done now. Its ok as long as you reference FractalForums as the source and me as the author of that code based on your code.

I would like to remove the wikibooks fragmentarium stuff as its out of date and wiki books doesn't give me the freedom I need to maintain it properly... they complain when I post a screenshot and tell me that I'm not allowed to post copyrighted material...FragM is opensource and I have contributed more than half of the code, so wikibooks is not the place I want people going for proper and up to date documentation.

I have a wiki on the github site that is up to date and would like the fragmentarium wikibooks page to link there instead.

Feel free to incorporate any improvements or optimizations Ive made into your own code.
« Last Edit: June 25, 2020, 01:11:10 AM by 3DickUlus »

• Fractal Frogurt
• Posts: 433
##### Re: Lagrangian Descriptors Fragment code
« Reply #7 on: June 25, 2020, 09:01:11 PM »
I didn't explicitly give permission to post the fragment code but its done now. Its ok as long as you reference FractalForums as the source and me as the author of that code based on your code.

I can remove the code, if you want it.

Quote
I would like to remove the wikibooks fragmentarium stuff as its out of date and wiki books doesn't give me the freedom I need to maintain it properly... they complain when I post a screenshot and tell me that I'm not allowed to post copyrighted material...FragM is opensource and I have contributed more than half of the code, so wikibooks is not the place I want people going for proper and up to date documentation.

I'm sad to hear it. Maybe it is a technical problem and it can be resolved ?

Quote
I have a wiki on the github site that is up to date and would like the fragmentarium wikibooks page to link there instead.
Ok

#### 3DickUlus

• Posts: 1975
##### Re: Lagrangian Descriptors Fragment code
« Reply #8 on: June 26, 2020, 01:56:52 AM »
oh no,  leave it there, everything I write for FragM is for the community, as I said, "Its ok as long as you reference FractalForums as the source and me as the author of that code based on your code."

Wikibooks has a purpose and provides great information but as soon as I publish something there it's no longer mine and it seems I need someone else's permission or review or whatever before it's actually put on the page. Wikibooks is imho not a place for program documentation, it is a place for a user to write about things they've done or learned or maybe a tutorial/how-to but the actual program  documentation must remain attached to the program and must not subject to approval by someone who may know nothing about the program or programming.

The material that you've gathered on wikibooks is great, it's really nice to have that as a reference.  your efforts are greatly appreciated.

I've found that with the GLSL the second lower/interior test is not required and it renders  the same image, I've also optimized it a little further, the main function is just the standard mandelbrot so moved all that code into the vec3 color(vec2 c) function and the float ppnorm( vec2 z, vec2 c, float p) function is only 6 lines of actual code that does the work, 8 with decls...
Code: [Select]
float ppnorm( vec2 z, vec2 c, float p){ vec3 s0,s1; // for 2 points on the Riemann sphere float d; // denominator // map from complex plane to riemann sphere // z d = z.x*z.x + z.y*z.y + 1.0; s0 = vec3(z,(d-2.0))/d; // c d = c.x*c.x + c.y*c.y + 1.0; s1 = vec3(c,(d-2.0))/d; // sum vec3 ss = pow(abs(s1 - s0),vec3(p)); return ss.x+ss.y+ss.z;}// DLD = Discret Lagrangian Descriptiorvec3 color(vec2 c) { vec2 z = Julia ? c : vec2(0.,0.); int i; // number of iterations float d = 0.0; // DLD = sum if(Julia) c = JuliaXY; for (i=0; i<Iterations; ++i){ d += ppnorm(z, c, p); // sum z z = cMul(z,z) +c; // complex iteration if (length(z) > 1e+19 ) break; // upper limit of float type 3.402823466e+38 } float co = d / float(i); // averaging not summation return .5+.5*cos(6.2831*co+RGB);}... it runs at max fps... not sure of the exact number but well beyond 60fps on my GPU moving the ppnorm code into the main color function should speed it up a bit more but , depending on the gfx driver this may be redundant after the glsl compiler optimizes things.

• Fractal Frogurt
• Posts: 433
##### Re: Lagrangian Descriptors Fragment code
« Reply #9 on: June 29, 2020, 05:46:20 PM »
I like the possibility to change parameters and see the result in real time. It helps tuning the parameters. I can't do it with my c program

I have also found that changing p seems most important

Should I also check the code which is included ( Complex.frag, MathUtils.frag and Progressive2D.frag) to see why my image is different ?
« Last Edit: June 30, 2020, 05:31:49 PM by Adam Majewski, Reason: p »

#### 3DickUlus

• Posts: 1975
##### Re: Lagrangian Descriptors Fragment code
« Reply #10 on: June 30, 2020, 01:32:59 AM »
your second image looks exactly like mine just no color, the only fragment code that gets used from the included files for calculating values is the complex multiply function cMul() and it is just the standard complex multiply so I don't think any of the included code accounts for difference, (I don't see the difference)

and the fragment code is all 32bit float type while your C proggie is using 64bit double type, that may account for a small difference.

### Similar Topics

###### Colouring with Discrite Lagrangian Descriptors

Started by Sabine62 on Color Snippets

1 Replies
101 Views
December 09, 2020, 12:37:04 PM
by Sabine62
###### Unveiling the Fractal Structure of Julia Sets with Lagrangian Descriptors
60 Replies
2960 Views
June 26, 2020, 08:00:47 PM
###### Fragment repository

Started by CJR on Fragmentarium

6 Replies
371 Views
July 01, 2020, 07:20:41 AM
by 3DickUlus
###### Apollonian fragment

Started by CJR on Fragmentarium

5 Replies
422 Views
November 20, 2018, 05:44:06 PM
by Sabine62