Fractal （分形）

A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales. The object need not exhibit exactly the same structure at all scales, but the same "type" of structures must appear on all scales.
A box fractal is defined as below : 

• A box fractal of degree 1 is simply 
  X 
  
• A box fractal of degree 2 is 
  X X 
  X 
  X X 
  
• If using B(n - 1) to represent the box fractal of degree n - 1, then a box fractal of degree n is defined recursively as following 
  

  B(n - 1)        B(n - 1)
  
          B(n - 1)
  
  B(n - 1)        B(n - 1)

Your task is to draw a box fractal of degree n.

Input

The input consists of several test cases. Each line of the input contains a positive integer n which is no greater than 7. The last line of input is a negative integer −1 indicating the end of input.

Output

For each test case, output the box fractal using the 'X' notation. Please notice that 'X' is an uppercase letter. Print a line with only a single dash after each test case.

Sample Input

1
2
3
4
-1

Sample Output

X
-
X X
 X
X X
-
X X   X X
 X     X
X X   X X
   X X
    X
   X X
X X   X X
 X     X
X X   X X
-
X X   X X         X X   X X
 X     X           X     X
X X   X X         X X   X X
   X X               X X
    X                 X
   X X               X X
X X   X X         X X   X X
 X     X           X     X
X X   X X         X X   X X
         X X   X X
          X     X
         X X   X X
            X X
             X
            X X
         X X   X X
          X     X
         X X   X X
X X   X X         X X   X X
 X     X           X     X
X X   X X         X X   X X
   X X               X X
    X                 X
   X X               X X
X X   X X         X X   X X
 X     X           X     X
X X   X X         X X   X X
-

分形递归

dfs的一种n==1的时候递归的深度到底然后将点赋值为X

每一个点都可以分为下一层的图形

举这个题的例子

xxx()函数是存储3 的几次幂

每一重的时候五个点的关系的距离是按照层数递减

 int d=xxx(n-2);
    dfs(n-1,x,y);
    dfs(n-1,x,y+2*d);
    dfs(n-1,x+d,y+d);
    dfs(n-1,x+2*d,y);
    dfs(n-1,x+2*d,y+2*d);

每个点细分为5个点

#include<stdio.h>
#include<string.h>
#include<algorithm>
using namespace std;
char s[1003][1003];
int xxx(int n)
{
    int ans=1;
    for(int i=1; i<=n; i++)
        ans*=3;
    return ans;
}
void dfs(int n,int x,int y)
{
    if(n==1)
    {
        s[x][y]='X';
        return;
    }
    int d=xxx(n-2);
    dfs(n-1,x,y);
    dfs(n-1,x,y+2*d);
    dfs(n-1,x+d,y+d);
    dfs(n-1,x+2*d,y);
    dfs(n-1,x+2*d,y+2*d);
}
int main()
{
    int n;
    while(~scanf("%d",&n))
    {
        if(n==-1)
            break;
        int d=xxx(n-1);
        for(int i=0;i<d;i++)
        {
            for(int j=0;j<d;j++)
                s[i][j]=' ';
        }
        dfs(n,0,0);
        for(int i=0;i<d;i++)
        {
            for(int j=d;j>=0;j--)
            {
                if(s[i][j]=='X')
                {
                    s[i][j+1]='\0';
                    break;
                }
            }
        }
        for(int i=0;i<d;i++)
            printf("%s\n",s[i]);
        printf("-\n");
    }
}