Python – how to programtically build a grid of interlocking but random sized squares

mathprogramming practicespython

I want to create a two dimensional layout of rectangular shapes, a grid made up of random sized cubes. The cubed should fit together and have equal padding or margin (space between). Kind of like a comic book layout, or more like the image attached.

How could I do this procedurally?

Practically, I would probably be using Python and some graphic software to render an image, but I don't know the type of algorithm (or whatnot) I would need to use to generate the randomized grid.

random cubes

Best Answer

Start with a grid of 1x1 cells. Pick a random spot, merge cells a random amount or till it collides with a larger rectangle.

This will get you something similar to the image you provide.

There's a bigger issues if you don't want a number of smaller cells acting as padding between your bigger cells. A comic book for example, wants to minimize the amount of dead space and have at most ~9 cells. You could pick some points and draw some lines and call those your cells. 

//Philip Haubrich, 2012, public domain
//Build instructions: gcc comicPanels.c

#include <stdio.h>  //entirely for printf()
#include <stdlib.h> //Entirely for rand()
#include <time.h> //Entirely to help srand()

#define PAINTINGSIZE_X 79
#define PAINTINGSIZE_Y 20

#define MYNUMBEROFPOINTS 4

#define MINDISTANCEBETWEENBOXES 2
//Because I suck at naming things. You should really fix this before it gets into your codebase.

#define NORTH 0
#define EAST 1
#define SOUTH 2
#define WEST 3

#define WHITE 0
#define BLACK 1

//Or, you know, a struct with .color, .r .g .b .alpha .editablebydeadpool
char g_paintingArea[PAINTINGSIZE_X][PAINTINGSIZE_Y];

void drawLineUntilBlocked(int x, int y, int direction)
{
  do
  {
    g_paintingArea[x][y] = BLACK;
    switch(direction)
    {
    case NORTH:
      y++;
      break;
    case SOUTH:
      y--;
      break;
    case EAST:
      x++;
      break;
    case WEST:
      x--;
      break;
    default:
      printf("I really need to get away from switch statements...\n");
    }
  } while(g_paintingArea[x][y] == WHITE && x > 0 && y > 0 && x < PAINTINGSIZE_X && y < PAINTINGSIZE_Y);
  //dowhile, when you are too lazy to re-arrange the code
}

//Feel free to sub in something like SDL or openGL here
void paint()
{
  int x,y;
  for(y=0; y<PAINTINGSIZE_Y; y++)
  {
    for(x=0; x<PAINTINGSIZE_X; x++)
    {
      printf("%c",g_paintingArea[x][y]);
    }
    printf("\n");
  }
}

int empty(int origx, int origy)
{
  int x,y;
  for(x=origx-MINDISTANCEBETWEENBOXES; x<origx+MINDISTANCEBETWEENBOXES; x++)
  {
    for(y=origy-MINDISTANCEBETWEENBOXES; y<origy+MINDISTANCEBETWEENBOXES; y++)
    { 
      if( x < 0 || y < 0 || x >= PAINTINGSIZE_X || y >= PAINTINGSIZE_Y)
        continue;
      if( g_paintingArea[x][y] == BLACK)
        return 0; //Not empty, there is something nearby
    }
  }
  return 1; //Empty, like my heart
}

void init()
{
  int x,y;
  //initalize to zero
  for(x=0; x<PAINTINGSIZE_X; x++)
  {
    for(y=0; y<PAINTINGSIZE_Y; y++)
    {
      g_paintingArea[x][y] = WHITE;
    }
  }
  //Border, or as I like to call it B-town
  for(x=0; x<PAINTINGSIZE_X; x++)
  {
    g_paintingArea[x][0] = BLACK;
    g_paintingArea[x][PAINTINGSIZE_Y-1] = BLACK;
  }
  for(y=0; y<PAINTINGSIZE_Y; y++)
  {
    g_paintingArea[0][y] = BLACK;
    g_paintingArea[PAINTINGSIZE_X-1][y] = BLACK;
  }

  //oh yeah, this is important
  x = abs(time(NULL));
  srand(x);
}

int main(int argc, char** argv)
{
  int x,y,i; 

  init();

  //That part you actually asked about
  for( i=0; i<MYNUMBEROFPOINTS; i++)
  {
    x = rand() % PAINTINGSIZE_X;
    y = rand() % PAINTINGSIZE_Y;

    if(!empty(x,y))
      continue;

    switch(rand()%3)
    {
    case 0: //4 way
      drawLineUntilBlocked(x,y,NORTH);
      drawLineUntilBlocked(x,y,SOUTH);
      drawLineUntilBlocked(x,y,EAST);
      drawLineUntilBlocked(x,y,WEST);
      break;
    case 1: //North/sourth
      drawLineUntilBlocked(x,y,NORTH);
      drawLineUntilBlocked(x,y,SOUTH);
      break;
    case 2: //East/West
      drawLineUntilBlocked(x,y,EAST);
      drawLineUntilBlocked(x,y,WEST);
      break;
    default:
      printf("Oh god wtf, and other useful error messages\n");
    }
  }
  //If I have to explain to you that this next bit will depend on your platform, then programming may not be for you
  paint();  
  return 0;
}

There are plenty more way to skin a cat.

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