数学之美，C++之美，代码之美
2024-04-02 23:57:50
用三段 140 字符以内的代码生成一张 1024×1024 的图片
Kyle McCormick 在 StackExchange 上发起了一个叫做 Tweetable Mathematical Art 的比赛，参赛者需要用三条推这么长的代码来生成一张图片。具体地说，参赛者需要用 C++ 语言编写 RD 、 GR 、 BL 三个函数，每个函数都不能超过 140 个字符。每个函数都会接到 i 和 j 两个整型参数（0 ≤ i, j ≤ 1023），然后需要返回一个 0 到 255 之间的整数，表示位于 (i, j) 的像素点的颜色值。举个例子，如果 RD(0, 0) 和 GR(0, 0) 返回的都是 0 ，但 BL(0, 0) 返回的是 255 ，那么图像的最左上角那个像素就是蓝色。参赛者编写的代码会被插进下面这段程序当中（我做了一些细微的改动），最终会生成一个大小为 1024×1024 的图片。
// 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 rootunsigned 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);
}1.第一个是 Martin Büttner 的作品
(由于其生成的是ppm格式的图片，电脑普通工具无法查看，故修改了使用opencv查看)
// opencv_2Dcode.cpp : 定义控制台应用程序的入口点。
//#include "stdafx.h"#include <iostream>
#include <cmath>
#include <cstdlib>
#include<string>
#include<opencv2\highgui\highgui.hpp>
#include<opencv2\opencv.hpp>
#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 rootunsigned char RD(int, int);
unsigned char GR(int, int);
unsigned char BL(int, int);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);cv::Mat srcImage = cv::imread("MathPic.ppm", 1);cv::imwrite("MathPic.jpg", srcImage);cv::imshow("MathPic.ppm", srcImage);cvWaitKey(0);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);
}unsigned char RD(int i, int j) {// YOUR CODE HEREreturn (char)(_sq(cos(atan2(j - 512, i - 512) / 2 * 255)));
}
unsigned char GR(int i, int j) {// YOUR CODE HEREreturn (char)(_sq(cos(atan2(j - 512, i - 512) / 2 - 2 * acos(-1) / 3)) * 255);
}
unsigned char BL(int i, int j) {// YOUR CODE HEREreturn (char)(_sq(cos(atan2(j - 512, i - 512) / 2 + 2 * acos(-1) / 3)) * 255);
}
2.第二个也是Martin Büttner 的作品
// opencv_2Dcode.cpp : 定义控制台应用程序的入口点。
//#include "stdafx.h"#include <iostream>
#include <cmath>
#include <cstdlib>
#include<string>
#include<opencv2\highgui\highgui.hpp>
#include<opencv2\opencv.hpp>
#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 rootunsigned char RD(int, int);
unsigned char GR(int, int);
unsigned char BL(int, int);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);cv::Mat srcImage = cv::imread("MathPic.ppm", 1);cv::imwrite("MathPic.jpg", srcImage);cv::imshow("MathPic.ppm", srcImage);cvWaitKey(0);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);
}unsigned char RD(int i, int j) {// YOUR CODE HERE// return (char)(_sq(cos(atan2(j - 512, i - 512) / 2 * 255)));
#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) {// YOUR CODE HERE// return (char)(_sq(cos(atan2(j - 512, i - 512) / 2 - 2 * acos(-1) / 3)) * 255);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) {// YOUR CODE HERE// return (char)(_sq(cos(atan2(j - 512, i - 512) / 2 + 2 * acos(-1) / 3)) * 255);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];
}
3.还是出自Martin Büttner 之手
// opencv_2Dcode.cpp : 定义控制台应用程序的入口点。
//#include "stdafx.h"#include <iostream>
#include <cmath>
#include <cstdlib>
#include<string>
#include<opencv2\highgui\highgui.hpp>
#include<opencv2\opencv.hpp>
#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 rootunsigned char RD(int, int);
unsigned char GR(int, int);
unsigned char BL(int, int);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);cv::Mat srcImage = cv::imread("MathPic.ppm", 1);cv::imwrite("MathPic.jpg", srcImage);cv::imshow("MathPic.ppm", srcImage);cvWaitKey(0);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);
}unsigned char RD(int i, int j) {// YOUR CODE HEREfloat 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) {// YOUR CODE HEREfloat 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) {// YOUR CODE HEREfloat 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 也制作了一个 Mandelbrot 集的图片，与刚才不同的是，该图描绘的是 Mandelbrot 集在某处局部放大后的结果：
// opencv_2Dcode.cpp : 定义控制台应用程序的入口点。
//#include "stdafx.h"#include <iostream>
#include <cmath>
#include <cstdlib>
#include<string>
#include<opencv2\highgui\highgui.hpp>
#include<opencv2\opencv.hpp>
#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 rootunsigned char RD(int, int);
unsigned char GR(int, int);
unsigned char BL(int, int);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);cv::Mat srcImage = cv::imread("MathPic.ppm", 1);cv::imwrite("MathPic.jpg", srcImage);cv::imshow("MathPic.ppm", srcImage);cvWaitKey(0);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);
}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);
}
4.这是 Manuel Kasten 的另一作品：
生成这张图片的代码很有意思：函数依靠 static 变量来控制绘画的进程，完全没有用到 i 和 j 这两个参数。
// opencv_2Dcode.cpp : 定义控制台应用程序的入口点。
//#include "stdafx.h"#include <iostream>
#include <cmath>
#include <cstdlib>
#include<string>
#include<opencv2\highgui\highgui.hpp>
#include<opencv2\opencv.hpp>
#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 rootunsigned char RD(int, int);
unsigned char GR(int, int);
unsigned char BL(int, int);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);cv::Mat srcImage = cv::imread("MathPic.ppm", 1);cv::imwrite("MathPic.jpg", srcImage);cv::imshow("MathPic.ppm", srcImage);cvWaitKey(0);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);
}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;
}
5.这是来自 githubphagocyte 的作品：
// opencv_2Dcode.cpp : 定义控制台应用程序的入口点。
//#include "stdafx.h"#include <iostream>
#include <cmath>
#include <cstdlib>
#include<string>
#include<opencv2\highgui\highgui.hpp>
#include<opencv2\opencv.hpp>
#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 rootunsigned char RD(int, int);
unsigned char GR(int, int);
unsigned char BL(int, int);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);cv::Mat srcImage = cv::imread("MathPic.ppm", 1);cv::imwrite("MathPic.jpg", srcImage);cv::imshow("MathPic.ppm", srcImage);cvWaitKey(0);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);
}unsigned char RD(int i, int j) {
#define P 6.03float s = 3. / (j + 250), y = (j + sin((i*i + _sq(j - 700) * 5) / 100. / DIM + P) * 15)*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 + 250);float y = (j + sin((i*i + _sq(j - 700) * 5) / 100. / DIM + P) * 15)*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 + 250);float y = (j + sin((i*i + _sq(j - 700) * 5) / 100. / DIM + P) * 15)*s;return (int(29 * ((i + DIM)*s + y)) % 2 + int(29 * ((DIM * 2 - i)*s + y)) % 2) * 127;
}
6.很有意思的一个代码：
// opencv_2Dcode.cpp : 定义控制台应用程序的入口点。
//#include "stdafx.h"#include <iostream>
#include <cmath>
#include <cstdlib>
#include<string>
#include<opencv2\highgui\highgui.hpp>
#include<opencv2\opencv.hpp>
#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 rootunsigned char RD(int, int);
unsigned char GR(int, int);
unsigned char BL(int, int);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);cv::Mat srcImage = cv::imread("MathPic.ppm", 1);cv::imwrite("MathPic.jpg", srcImage);cv::imshow("MathPic.ppm", srcImage);cvWaitKey(0);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);
}unsigned char RD(int i, int j) {return BL(i, j) * 2;#define t(m,n)_sq(m)+_sq(n)#define z(m,n)t(m*32-i,n*32-j)#define q(m,n,k)if(z(m,n)<196)return k*255;if(z(m,n)<225)return 0;
}unsigned char GR(int i, int j) {return BL(i, j);
}unsigned char BL(int i, int j) {q(16, 16, 1)q(15, 16, 0)q(16, 15, 0)q(17, 16, 0)q(16, 17, 0)return(i & 31) && (j & 31) ? 80 : 0;
}
7.这是个模拟放大镜的效果，加入模拟波纹的话，非常nice
// opencv_2Dcode.cpp : 定义控制台应用程序的入口点。
//#include "stdafx.h"#include <iostream>
#include <cmath>
#include <cstdlib>
#include<string>
#include<opencv2\highgui\highgui.hpp>
#include<opencv2\opencv.hpp>
#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 rootunsigned char RD(int, int);
unsigned char GR(int, int);
unsigned char BL(int, int);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);cv::Mat srcImage = cv::imread("MathPic.ppm", 1);cv::imwrite("MathPic.jpg", srcImage);cv::imshow("MathPic.ppm", srcImage);cvWaitKey(0);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);
}unsigned char RD(int i, int j) {#define F(x) float x#define R return#define Ci (DIM/2)#define Cj Ci#define Z (Ci/2)#define G (Ci/8)#define N 3R BL(i, j);
}unsigned char GR(int i, int j) {#define Y(x) sqrt(1.-_sq(x))R BL(i, j);
}unsigned char BL(int i, int j) {F(r) = sqrt(0. + _sq(i - Ci) + _sq(j - Cj)); F(s) = r / Z; if (s<1) { i -= Ci; j -= Cj; F(k) = (Y(s)*Y(s / N) + _sq(s) / N)*N; i = i / k + Ci; j = j / k + Cj; }R(i / G + j / G) % 2 * 255;
}
8.来一张密集恐怖的
// opencv_2Dcode.cpp : 定义控制台应用程序的入口点。
//#include "stdafx.h"#include <iostream>
#include <cmath>
#include <cstdlib>
#include<string>
#include<opencv2\highgui\highgui.hpp>
#include<opencv2\opencv.hpp>
#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 rootunsigned char RD(int, int);
unsigned char GR(int, int);
unsigned char BL(int, int);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);cv::Mat srcImage = cv::imread("MathPic.ppm", 1);cv::imwrite("MathPic.jpg", srcImage);cv::imshow("MathPic.ppm", srcImage);cvWaitKey(0);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);
}unsigned char RD(int i, int j) {// *2 expand the spiral// DIM- reverse the gradientreturn DIM - BL(2 * i, 2 * j);
}
unsigned char GR(int i, int j) {// notice swapped parameters// 128 changes phase of the spiralreturn BL(j, i) + 128;
}
unsigned char BL(int i, int j) {// center iti -= DIM / 2;j -= DIM / 2;double theta = atan2(j, i); //angle that point is from centerdouble prc = theta / 3.14f / 2.0f; // percent around the circleint dist = sqrt(i*i + j*j); // distance from center// EDIT: if you change this to something like "prc * n * 256" where n// is an integer, the spirals will line up for any arbitrarily sized// DIM value, or if you make separate DIMX and DIMY values!int makeSpiral = prc * DIM / 2;// makes pattern on edge of the spiralint waves = sin(_cr(dist * dist)) * 32 + sin(theta * 10) * 64;return dist + makeSpiral + waves;
}
9.最后来一张中和的，太极八卦阵
// opencv_2Dcode.cpp : 定义控制台应用程序的入口点。
//#include "stdafx.h"#include <iostream>
#include <cmath>
#include <cstdlib>
#include<string>
#include<opencv2\highgui\highgui.hpp>
#include<opencv2\opencv.hpp>
#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 rootunsigned char RD(int, int);
unsigned char GR(int, int);
unsigned char BL(int, int);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);cv::Mat srcImage = cv::imread("MathPic.ppm", 1);cv::imwrite("MathPic.jpg", srcImage);cv::imshow("MathPic.ppm", srcImage);cvWaitKey(0);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);
}unsigned char RD(int i, int j) {// YOUR CODE HERE
#define LEFT (i < DIM/2)
#define C1 C(DIM/2, DIM/2, DIM/2)
#define C2 C(DIM/2, DIM/4, DIM/4) return BL(i, j);
}
unsigned char GR(int i, int j) {// YOUR CODE HERE
#define C3 C(DIM/2, 3*DIM/4, DIM/4)
#define C4 C(DIM/2, DIM/4, DIM/16)
#define C5 C(DIM/2, 3*DIM/4, DIM/16) return BL(i, j);
}
unsigned char BL(int i, int j) {// YOUR CODE HERE
#define C(x, y, r) (_sq(i - (x)) + _sq(j - (y)) < _sq((r))) return !C1 ? 127 : C2 ? C4 ? 0 : 255 : C3 ? C5 ? 255 : 0 : LEFT ? 255 : 0;
}
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