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Markus-Lyapunov Fractal


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Posted (edited)

I might or might not finish this though. I'm working on Markus-Lyapunov as a C# plugin. If I decide not to finish it up, then I'll be leaving this for others to complete.

 

Random option is just a gradient of random color, and double palettes there mean two gradients.

 

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// Name: Markus-Lyapunov Fractal
// Submenu: Render
// Author: Reptorian
// Title: Markus-Lyapunov Fractal
// Version: .5
// Desc: Generates Markus-Lyapunov Fractal
// Keywords: Fractal
// URL: https://forums.getpaint.net/profile/85868-reptillian/?ct=1626304395
// Help:
#region UICode
TextboxControl str_var = "ab"; // [255] ABC-String
IntSliderControl abc_repeats = 50; // [1,100] ABC-String Repeats
DoubleSliderControl view_size = 100; // [0.1,100] View Size (%)
PanSliderControl view_pos = Pair.Create(0.000, 0.000); // View Position
DoubleSliderControl c_pos = 0; // [-1,1] C Position
ListBoxControl output_mode = 1; // Mode|Default|Duotone
CheckboxControl revert_mode = false; // Reverted Mode
ColorWheelControl color_a = ColorBgra.FromBgr(255, 0, 0); // [Blue] Color A
ColorWheelControl color_b = ColorBgra.FromBgr(0, 255, 255); // [Yellow] Color B
#endregion
#if DEBUG
#endif
int[] i_var;
int s_str_var;
bool validity;
double[,] Lyapunov_Surface;

double iM;
double im;
double hpi = Math.PI*2;

/*

The C# code below is to use for randomized palette mode. Only kept it here for future development.
double[] hue;
double[] saturation;
double[] intensity;
*/

double contrast(double a){
    double b=a*Math.PI-hpi;
    return .5*(a*a)+.5*(Math.Sin(b)+1)/2;
}

/*

The C# code below is to use for randomized palette mode. Only kept it here for future development.

double rescale(double a,double b){
    double i = a + b ;
    return i * 765;
}

ColorBgra RGB_from_HSI(double hue, double saturation, double intensity){
    int H = ((int)(hue)/60)%6;
    int Z = 1 - Math.Abs((H%2)-1);
    double C = intensity * saturation / (1 + (double)(Z));
    double X = C * (double)(Z);
    double m = intensity * (1 - saturation)/3;
    byte red = 0;
    byte green = 0;
    byte blue = 0;

    switch(H){
        case 0:
         red = (byte)((int)(rescale(C,m)));
         green = (byte)((int)(rescale(X,m)));
         blue = (byte)(rescale(0,m));
         break;
        case 1: 
         red = (byte)((int)(rescale(X,m)));
         green = (byte)((int)(rescale(C,m)));
         blue = (byte)(rescale(0,m));
         break;
        case 2: 
         red = (byte)(rescale(0,m));
         green = (byte)((int)(rescale(C,m)));
         blue = (byte)((int)(rescale(X,m)));
         break;
        case 3: 
         red = (byte)(rescale(0,m));
         green = (byte)((int)(rescale(X,m)));
         blue = (byte)((int)(rescale(C,m)));
         break;
        case 4: 
         red = (byte)((int)(rescale(C,m)));
         green = (byte)(rescale(0,m));
         blue = (byte)((int)(rescale(X,m)));
         break;
        case 5: 
         red = (byte)((int)(rescale(X,m)));
         green = (byte)(rescale(0,m));
         blue = (byte)((int)(rescale(C,m)));
         break;
    }

    return ColorBgra.FromBgr(blue,green,red);
}
*/

double lerp(double a, double b, double t){
    return a * (1 - t) + b * t ;
}

void PreRender(Surface dst, Surface src){

    int w = src.Width;
    int h = src.Height;
    int inc_w = w + 1;
    int inc_h = h + 1;

    if (Lyapunov_Surface == null){Lyapunov_Surface = new double [w,h];}
    else {Array.Clear(Lyapunov_Surface, 0, w*h);}

    s_str_var = str_var.Length;
    char[] charArr=str_var.ToCharArray();
    i_var = new int[s_str_var];
    char temp_char;
    validity = true;

    bool a_valid = false ;
    bool b_valid = false ;

    if (s_str_var==0){
        validity = false;
        return;
    }

    for(int pos = 0 ; pos < s_str_var ; pos++){
        temp_char=Char.ToLower(charArr[pos]);
        i_var[pos]=(int) charArr[pos] - 97;
        if (i_var[pos]<0||i_var[pos]>2){
            validity = false;
            break;
        }
        else{
            switch(i_var[pos]){
                case 0:
                    a_valid = true;
                    break;
                case 1:
                    b_valid = true;
                    break;
                default:
                    break;
            }
        }
    }

    if (!a_valid||!b_valid){
        validity = false;
        return;
    }

    float sqr_size = (float)(view_size /100);
    float gap = 1 - sqr_size ;
    float px = (float)((view_pos.First + 1) / 2);
    float py = (float)((view_pos.Second*-1 + 1) / 2);
    px*=gap;
    py*=gap;
    float lx = px * 2 + 2;
    float ly = py * 2 + 2;
    float rx = (px + sqr_size) * 2 + 2;
    float ry = (py + sqr_size) * 2 + 2;
    double md = Math.Max(w,h);
    double iz = lerp(2+1/(md+1),2+(md/(md+1))*2,(float)(c_pos));

    int total_string_length = s_str_var  * abc_repeats;
    int sp;

    double cx,cy,ix,iy,vn,limit,rn;

    im=0;
    iM=0;

    float f_inc_w = (float)(inc_w+1);
    float f_inc_h = (float)(inc_h+1);

    for(int x = 0 ; x < w ; x++){
        for(int y = 0 ; y < h ; y++){
            cx = (double)(x + 1);
            cy = (double)(y + 1);
            ix = lerp(lx,rx,cx/f_inc_w);
            iy = lerp(ry,ly,cy/f_inc_h);
            vn = .5f;
            limit = 0;
            for (int n = 0 ; n < total_string_length ; n++){
                sp = n % s_str_var;
                sp = i_var[sp];
                switch(sp){
                    case 0:rn=ix;break;
                    case 1:rn=iy;break;
                    case 2:rn=iz;break;
                    default:rn=1;break;
                }
                vn=rn*vn*(1-vn);
                limit+=(float)(Math.Log(Math.Abs((double)(rn*(1-2*vn)))));
            }
            if(limit < im) {im = limit;}
            if(limit > iM) {iM = limit;}
            Lyapunov_Surface[x,y] = limit;
        }
    }
}

void Render(Surface dst, Surface src, Rectangle rect)
{
    // Delete any of these lines you don't need
    int thick = src.Width / s_str_var;
    int represent;
    byte r;

    double tv,shade,t_shade;
    double rescale_factor = (iM-im)/255f;

    double d_r_a = (double)(color_a[2]);
    double d_g_a = (double)(color_a[1]);
    double d_b_a = (double)(color_a[0]);

    double d_r_b = (double)(color_b[2]);
    double d_g_b = (double)(color_b[1]);
    double d_b_b = (double)(color_b[0]);

    double nr,ng,nb;

    if (validity){
        rescale_factor = (iM-im)/255f;
    }
    else{
        rescale_factor = 1;
    }

    for (int y = rect.Top; y < rect.Bottom; y++)
    {
        if (IsCancelRequested) return;
        for (int x = rect.Left; x < rect.Right; x++)
        {
            switch(output_mode){
                case 0:
                    tv = (Lyapunov_Surface[x,y]-im)/(rescale_factor);
                    if (revert_mode){
                        represent = 255 -(int)(tv);
                    }
                    else{
                        represent = (int)(tv);
                    }
                    r = (byte)(represent);
                    dst[x,y] = ColorBgra.FromBgraClamped(r,r,r,255);
                    
                    break;
                case 1:
                    if(Lyapunov_Surface[x,y] >= 0){
                        shade = Lyapunov_Surface[x,y] / iM;
                        nr = d_r_a * shade;
                        ng = d_g_a * shade;
                        nb = d_b_a * shade;
                    }
                    else{
                        shade = Math.Pow(1 - Lyapunov_Surface[x,y] / im,3);
                        nr = d_r_b * shade;
                        ng = d_g_b * shade;
                        nb = d_b_b * shade;
                    }

                    dst[x,y] = ColorBgra.FromBgraClamped((byte)((int)(nb)),(byte)((int)(ng)),(byte)((int)(nr)),255);
                    break;
            }
        }
    }
}

 

 

Edited by Reptillian

G'MIC Filter Developer

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Posted (edited)

I had just updated code above. Even left some code sample to be used for HSI palette being the base for coloring the Lyapunov Fractal. Though, just from this, I find that the code is really slow. I know this is because that it is single-threaded. Doesn't look like there's much I can do about certain issues besides going into making it a gmic-pdn plugin though I prefer to avoid that route unless there's not a choice.

 

Issues:

1. Slow speed because of it being single-threaded.

2. Lack of random HSI palette mapping.

3. The C percentage gui element cannot be grayed out if there is no 'c' in abc-string.

4. Lack of anti-aliasing.

 

1,2,and 4 is solved by the gmic-pdn route. 3 isn't solve-able though @midora might have an answer to that via option-based library.

Edited by Reptillian

G'MIC Filter Developer

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