Programmers, what are your skills in code writing?

Manuel Kasten Also made a Mandelbrot Set of pictures , What's different from just now is , The picture depicts Mandelbrot The result of local amplification set somewhere ： We know , The color to be displayed in the computer , It's usually used R、G、B Three 0-255 An integer within a range to describe .

This point , Even if you're not in the front end 、 client These development work related to interface interaction , I should know .

in other words , The color of any pixel you see on the screen now , Both can be used. RGB Three integer values to represent .

Then there is an interesting question ： If you let the program automatically fill in each pixel , What will be the last picture ？

Recently, I saw such an interesting topic in Zhihu , It's really amazing after reading it , It is much joyful to share the joy than enjoy alone. , Share with you .

There is a big man abroad StackExchange There's a program called Tweetable Mathematical Art The game .

Contestants need to use C++ Write a code representing the three primary colors RD、GR、BL Three functions , Each function cannot exceed 140 Characters . Every function receives i and j Two integer parameters （0 ≤ i, j ≤ 1023）, Then you need to go back to a 0 To 255 Integer between , Means located at (i, j) The color value of the pixel .

for instance , If RD(0, 0) and GR(0, 0) All of them 0 , but BL(0, 0) The return is 255 , Then the pixel at the top left corner of the image is blue . The code written by the contestant will be inserted into the following program （ I made some minor changes ）, Finally, a size of 1024×1024 Pictures of the .

// NOTE: compile with g++ filename.cpp -std=c++11
#include <iostream>
#include <cmath>
#include <cstdlib>
#define DIM 1024
#define DM1 (DIM-1)
#define _sq(x) ((x)*(x)) // square
#define _cb(x) abs((x)*(x)*(x)) // absolute value of cube
#define _cr(x) (unsigned char)(pow((x),1.0/3.0)) // cube root
 
unsigned char GR(int,int);
unsigned char BL(int,int);
 
unsigned char RD(int i,int j){
   // YOUR CODE HERE
}
unsigned char GR(int i,int j){
   // YOUR CODE HERE
}
unsigned char BL(int i,int j){
   // YOUR CODE HERE
}
 
void pixel_write(int,int);
FILE *fp;
int main(){
    fp = fopen("MathPic.ppm","wb");
    fprintf(fp, "P6\n%d %d\n255\n", DIM, DIM);
    for(int j=0;j<DIM;j++)
        for(int i=0;i<DIM;i++)
            pixel_write(i,j);
    fclose(fp);
    return 0;
}
void pixel_write(int i, int j){
    static unsigned char color[3];
    color[0] = RD(i,j)&255;
    color[1] = GR(i,j)&255;
    color[2] = BL(i,j)&255;
    fwrite(color, 1, 3, fp);
}

I chose some of my favorite works , Put it below to share with you . The first is one from Martin Büttner The works of ：

  The code is as follows ：

unsigned char RD(int i,int j){
  return (char)(_sq(cos(atan2(j-512,i-512)/2))*255);
}

unsigned char GR(int i,int j){
  return (char)(_sq(cos(atan2(j-512,i-512)/2-2*acos(-1)/3))*255);
}

unsigned char BL(int i,int j){
  return (char)(_sq(cos(atan2(j-512,i-512)/2+2*acos(-1)/3))*255);
}

Also from Martin Büttner The works of ：

 

unsigned char RD(int i,int j){
  #define r(n)(rand()%n)
  static char c[1024][1024];
  return!c[i][j]?c[i][j]=!r(999)?r(256):RD((i+r(2))%1024,(j+r(2))%1024):c[i][j];
}

unsigned char GR(int i,int j){
  static char c[1024][1024];
  return!c[i][j]?c[i][j]=!r(999)?r(256):GR((i+r(2))%1024,(j+r(2))%1024):c[i][j];
}

unsigned char BL(int i,int j){
  static char c[1024][1024];
  return!c[i][j]?c[i][j]=!r(999)?r(256):BL((i+r(2))%1024,(j+r(2))%1024):c[i][j];
}

The following picture is still from Martin Büttner In the hands of ：

   unimaginable , Mandelbrot Fractal graphics can be drawn with only such a little code

nsigned char RD(int i,int j){
  float x=0,y=0;int k;for(k=0;k++<256;){float a=x*x-y*y+(i-768.0)/512;y=2*x*y+(j-512.0)/512;x=a;if(x*x+y*y>4)break;}
  return log(k)*47;
}

unsigned char GR(int i,int j){
  float x=0,y=0;int k;for(k=0;k++<256;){float a=x*x-y*y+(i-768.0)/512;y=2*x*y+(j-512.0)/512;x=a;if(x*x+y*y>4)break;}
  return log(k)*47;
}

unsigned char BL(int i,int j){
  float x=0,y=0;int k;for(k=0;k++<256;){float a=x*x-y*y+(i-768.0)/512;y=2*x*y+(j-512.0)/512;x=a;if(x*x+y*y>4)break;}
  return 128-log(k)*23;
}

Manuel Kasten Also made a Mandelbrot Set of pictures , What's different from just now is , The picture depicts Mandelbrot The result of local amplification set somewhere ：

  The code is as follows ：

unsigned char RD(int i,int j){
  double a=0,b=0,c,d,n=0;
  while((c=a*a)+(d=b*b)<4&&n++<880)
  {b=2*a*b+j*8e-9-.645411;a=c-d+i*8e-9+.356888;}
  return 255*pow((n-80)/800,3.);
}

unsigned char GR(int i,int j){
  double a=0,b=0,c,d,n=0;
  while((c=a*a)+(d=b*b)<4&&n++<880)
  {b=2*a*b+j*8e-9-.645411;a=c-d+i*8e-9+.356888;}
  return 255*pow((n-80)/800,.7);
}

unsigned char BL(int i,int j){
  double a=0,b=0,c,d,n=0;
  while((c=a*a)+(d=b*b)<4&&n++<880)
  {b=2*a*b+j*8e-9-.645411;a=c-d+i*8e-9+.356888;}
  return 255*pow((n-80)/800,.5);
}

This is a Manuel Kasten Another work of ：

  The code for generating this picture is very interesting ： The function depends on static Variable to control the process of painting , It's not used at all i and j These two parameters ！

unsigned char RD(int i,int j){
  static double k;k+=rand()/1./RAND_MAX;int l=k;l%=512;return l>255?511-l:l;
}

unsigned char GR(int i,int j){
  static double k;k+=rand()/1./RAND_MAX;int l=k;l%=512;return l>255?511-l:l;
}

unsigned char BL(int i,int j){
  static double k;k+=rand()/1./RAND_MAX;int l=k;l%=512;return l>255?511-l:l;
}

This is from githubphagocyte The works of ：

The code is as follows ：

unsigned char RD(int i,int j){
  float s=3./(j+99);
  float y=(j+sin((i*i+_sq(j-700)*5)/100./DIM)*35)*s;
  return (int((i+DIM)*s+y)%2+int((DIM*2-i)*s+y)%2)*127;
}

unsigned char GR(int i,int j){
  float s=3./(j+99);
  float y=(j+sin((i*i+_sq(j-700)*5)/100./DIM)*35)*s;
  return (int(5*((i+DIM)*s+y))%2+int(5*((DIM*2-i)*s+y))%2)*127;
}

unsigned char BL(int i,int j){
  float s=3./(j+99);
  float y=(j+sin((i*i+_sq(j-700)*5)/100./DIM)*35)*s;
  return (int(29*((i+DIM)*s+y))%2+int(29*((DIM*2-i)*s+y))%2)*127;
}

This is from githubphagocyte Another piece of work of ：

  This is a picture using diffusion-limited aggregation The picture from the model , The program takes a lot of time to run . The code is very interesting ： Clever use of macro definitions , Breaking the boundary between functions , The word limit of the three pieces of code can be used together .

unsigned char RD(int i,int j){
#define D DIM
#define M m[(x+D+(d==0)-(d==2))%D][(y+D+(d==1)-(d==3))%D]
#define R rand()%D
#define B m[x][y]
return(i+j)?256-(BL(i,j))/2:0;
}

unsigned char GR(int i,int j){
#define A static int m[D][D],e,x,y,d,c[4],f,n;if(i+j<1){for(d=D*D;d;d--){m[d%D][d/D]=d%6?0:rand()%2000?1:255;}for(n=1
return RD(i,j);
}

unsigned char BL(int i,int j){
A;n;n++){x=R;y=R;if(B==1){f=1;for(d=0;d<4;d++){c[d]=M;f=f<c[d]?c[d]:f;}if(f>2){B=f-1;}else{++e%=4;d=e;if(!c[e]){B=0;M=1;}}}}}return m[i][j];
}

The last picture comes from Eric Tressler：

  This is from logistic Mapped Feigenbaum Bifurcation diagram . Just like before , The corresponding code also makes clever use of Macro definition To save characters ：

unsigned char RD(int i,int j){
#define A float a=0,b,k,r,x
#define B int e,o
#define C(x) x>255?255:x
#define R return
#define D DIM
R BL(i,j)*(D-i)/D;
}

unsigned char GR(int i,int j){
#define E DM1
#define F static float
#define G for(
#define H r=a*1.6/D+2.4;x=1.0001*b/D
R BL(i,j)*(D-j/2)/D;
}

unsigned char BL(int i,int j){
F c[D][D];if(i+j<1){A;B;G;a<D;a+=0.1){G b=0;b<D;b++){H;G k=0;k<D;k++){x=r*x*(1-x);if(k>D/2){e=a;o=(E*x);c[e][o]+=0.01;}}}}}R C(c[j][i])*i/D;
}

What about? , Just a few lines of code , Can draw such a gorgeous image , Do you have any idea of a big hole in your brain , You can copy the above code to have a try ！

resources & More in-depth readings ：

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