Langton's ant is a cellular automaton that models an ant sitting on a plane of cells, all of which are white initially, the ant facing in one of four directions.

Each cell can either be black or white.

The ant moves according to the color of the cell it is currently sitting in, with the following rules:

   If the cell is black, it changes to white and the ant turns left;
   If the cell is white, it changes to black and the ant turns right;
   The ant then moves forward to the next cell, and repeat from step 1.

This rather simple ruleset leads to an initially chaotic movement pattern, and after about 10000 steps, a cycle appears where the ant moves steadily away from the starting location in a diagonal corridor about 10 cells wide.
Conceptually the ant can then walk infinitely far away.



Task

Start the ant near the center of a 100x100 field of cells, which is about big enough to contain the initial chaotic part of the movement.

Follow the movement rules for the ant, terminate when it moves out of the region, and show the cell colors it leaves behind.



The problem has received some analysis; for more details, please take a look at the Wikipedia article   (a link is below)..



See also

   Wikipedia:   Langton's ant.


Related task

   Rosetta Code:   Conway's Game of Life.


 
#include <windows.h>
#include <string>
 
//--------------------------------------------------------------------------------------------------
using namespace std;
 
//--------------------------------------------------------------------------------------------------
const int BMP_SIZE = 600, CELL_SIZE = 4, GRID_SIZE = BMP_SIZE / CELL_SIZE;
const bool INFINIT_RUN = false;
 
enum cellState { WHITE, BLACK, ANT };
enum facing { NOR, EAS, SOU, WES };
enum state { RUNNING, RESTING };
 
//--------------------------------------------------------------------------------------------------
class myBitmap
{
public:
    myBitmap() : pen( NULL ) {}
    ~myBitmap()
    {
	DeleteObject( pen );
	DeleteDC( hdc );
	DeleteObject( bmp );
    }
 
    bool create( int w, int h )
    {
	BITMAPINFO	bi;
	ZeroMemory( &bi, sizeof( bi ) );
 
	bi.bmiHeader.biSize	   = sizeof( bi.bmiHeader );
	bi.bmiHeader.biBitCount	   = sizeof( DWORD ) * 8;
	bi.bmiHeader.biCompression = BI_RGB;
	bi.bmiHeader.biPlanes	   = 1;
	bi.bmiHeader.biWidth	   =  w;
	bi.bmiHeader.biHeight	   = -h;
 
	HDC dc = GetDC( GetConsoleWindow() );
	bmp = CreateDIBSection( dc, &bi, DIB_RGB_COLORS, &pBits, NULL, 0 );
	if( !bmp ) return false;
 
	hdc = CreateCompatibleDC( dc );
	SelectObject( hdc, bmp );
	ReleaseDC( GetConsoleWindow(), dc ); 
 
	width = w; height = h;
 
	return true;
    }
 
    void clear()
    {
	ZeroMemory( pBits, width * height * sizeof( DWORD ) );
    }
 
    void setPenColor( DWORD clr )
    {
	if( pen ) DeleteObject( pen );
	pen = CreatePen( PS_SOLID, 1, clr );
	SelectObject( hdc, pen );
    }
 
    void saveBitmap( string path )
    {
	BITMAPFILEHEADER fileheader;
	BITMAPINFO	 infoheader;
	BITMAP		 bitmap;
	DWORD		 wb;
 
	GetObject( bmp, sizeof( bitmap ), &bitmap );
 
	DWORD* dwpBits = new DWORD[bitmap.bmWidth * bitmap.bmHeight];
	ZeroMemory( dwpBits, bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD ) );
	ZeroMemory( &infoheader, sizeof( BITMAPINFO ) );
	ZeroMemory( &fileheader, sizeof( BITMAPFILEHEADER ) );
 
	infoheader.bmiHeader.biBitCount = sizeof( DWORD ) * 8;
	infoheader.bmiHeader.biCompression = BI_RGB;
	infoheader.bmiHeader.biPlanes = 1;
	infoheader.bmiHeader.biSize = sizeof( infoheader.bmiHeader );
	infoheader.bmiHeader.biHeight = bitmap.bmHeight;
	infoheader.bmiHeader.biWidth = bitmap.bmWidth;
	infoheader.bmiHeader.biSizeImage = bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD );
 
	fileheader.bfType    = 0x4D42;
	fileheader.bfOffBits = sizeof( infoheader.bmiHeader ) + sizeof( BITMAPFILEHEADER );
	fileheader.bfSize    = fileheader.bfOffBits + infoheader.bmiHeader.biSizeImage;
 
	GetDIBits( hdc, bmp, 0, height, ( LPVOID )dwpBits, &infoheader, DIB_RGB_COLORS );
 
	HANDLE file = CreateFile( path.c_str(), GENERIC_WRITE, 0, NULL, CREATE_ALWAYS, FILE_ATTRIBUTE_NORMAL, NULL );
	WriteFile( file, &fileheader, sizeof( BITMAPFILEHEADER ), &wb, NULL );
	WriteFile( file, &infoheader.bmiHeader, sizeof( infoheader.bmiHeader ), &wb, NULL );
	WriteFile( file, dwpBits, bitmap.bmWidth * bitmap.bmHeight * 4, &wb, NULL );
	CloseHandle( file );
 
	delete [] dwpBits;
    }
 
    HDC getDC() const     { return hdc; }
    int getWidth() const  { return width; }
    int getHeight() const { return height; }
 
private:
    HBITMAP bmp;
    HDC	    hdc;
    HPEN    pen;
    void   *pBits;
    int	    width, height;
};
//--------------------------------------------------------------------------------------------------
class Ant
{
public:
    Ant() 
    {
	_bmp.create( BMP_SIZE, BMP_SIZE );
	ZeroMemory( _grid, sizeof( _grid ) );
	RED_BRUSH = CreateSolidBrush( 255 );
	_antState = RUNNING;
    }
 
    ~Ant()
    {
	DeleteObject( RED_BRUSH );
    }
 
    void setPosition( int x, int y )
    {
	_sx = x; _sy = y;
	_facing = WES;
    }
 
    void mainLoop()
    {
	switch( _antState )
	{
	    case RUNNING:
	        simulate();
		// fall thru
	    case RESTING:
		display();
	}
    }
 
    void setHWND( HWND hwnd ) { _hwnd = hwnd; }
 
private:
    void simulate()
    {
	switch( _grid[_sx][_sy] )
	{
	    case BLACK:
		_grid[_sx][_sy] = WHITE;
		if( --_facing < NOR ) _facing = WES;
	    break;
	    case WHITE:
		_grid[_sx][_sy] = BLACK;
		if( ++_facing > WES ) _facing = NOR;
	}
	switch( _facing )
	{
	    case NOR: 
		if( --_sy < 0 )
		{
		    if( INFINIT_RUN ) _sy = GRID_SIZE - 1;
		    else _antState = RESTING;
		}
	    break;
	    case EAS:
		if( ++_sx >= GRID_SIZE )
		{
		    if( INFINIT_RUN ) _sx = 0;
		    else _antState = RESTING;
		}
	    break;
	    case SOU:
		if( ++_sy >= GRID_SIZE )
		{
		    if( INFINIT_RUN ) _sy = 0;
		    else _antState = RESTING;
		}
	    break;
	    case WES:
	        if( --_sx < 0 )
		{
		    if( INFINIT_RUN ) _sx = GRID_SIZE - 1;
		    else _antState = RESTING;
		}
	}
    }
 
    void display()
    {
        _bmp.clear();
 
        HBRUSH br; RECT rc;
        int xx, yy; HDC dc = _bmp.getDC();
 
        for( int y = 0; y < GRID_SIZE; y++ )
	    for( int x = 0; x < GRID_SIZE; x++ )
	    {
	        switch( _grid[x][y] )
	        {
		    case BLACK: br = static_cast<HBRUSH>( GetStockObject( BLACK_BRUSH ) ); break;
		    case WHITE: br = static_cast<HBRUSH>( GetStockObject( WHITE_BRUSH ) );
	        }
	        if( x == _sx && y == _sy ) br = RED_BRUSH;
 
	        xx = x * CELL_SIZE; yy = y * CELL_SIZE;
	        SetRect( &rc, xx, yy, xx + CELL_SIZE, yy + CELL_SIZE );
	        FillRect( dc, &rc, br );
	    }
 
        HDC wdc = GetDC( _hwnd );
        BitBlt( wdc, 0, 0, BMP_SIZE, BMP_SIZE, dc, 0, 0, SRCCOPY );
        ReleaseDC( _hwnd, wdc );
    }
 
    myBitmap _bmp;
    HWND     _hwnd;
    HBRUSH   RED_BRUSH;
    BYTE     _grid[GRID_SIZE][GRID_SIZE];
    int      _sx, _sy, _facing;
    state    _antState;
};
//--------------------------------------------------------------------------------------------------
class wnd
{
public:
    int wnd::Run( HINSTANCE hInst )
    {
	_hInst = hInst;
	_hwnd = InitAll();
 
	_ant.setHWND( _hwnd );
	_ant.setPosition( GRID_SIZE / 2, GRID_SIZE / 2 );
 
	ShowWindow( _hwnd, SW_SHOW );
	UpdateWindow( _hwnd );
 
	MSG msg;
	ZeroMemory( &msg, sizeof( msg ) );
	while( msg.message != WM_QUIT )
	{
	    if( PeekMessage( &msg, NULL, 0, 0, PM_REMOVE ) != 0 )
	    {
		TranslateMessage( &msg );
		DispatchMessage( &msg );
	    }
	    else
	    {
		_ant.mainLoop();
	    }
	}
	return UnregisterClass( "_LANGTONS_ANT_", _hInst );
    }
private:
    static int WINAPI wnd::WndProc( HWND hWnd, UINT msg, WPARAM wParam, LPARAM lParam )
    {
	switch( msg )
	{
	    case WM_DESTROY: PostQuitMessage( 0 ); break;
	    default:
		return DefWindowProc( hWnd, msg, wParam, lParam );
	}
	return 0;
    }
 
    HWND InitAll()
    {
	WNDCLASSEX wcex;
	ZeroMemory( &wcex, sizeof( wcex ) );
	wcex.cbSize	       = sizeof( WNDCLASSEX );
	wcex.style	       = CS_HREDRAW | CS_VREDRAW;
	wcex.lpfnWndProc   = ( WNDPROC )WndProc;
	wcex.hInstance     = _hInst;
	wcex.hCursor       = LoadCursor( NULL, IDC_ARROW );
	wcex.hbrBackground = ( HBRUSH )( COLOR_WINDOW + 1 );
	wcex.lpszClassName = "_LANGTONS_ANT_";
 
	RegisterClassEx( &wcex );
 
	return CreateWindow( "_LANGTONS_ANT_", ".: Langton's Ant -- PJorente :.", WS_SYSMENU, CW_USEDEFAULT, 0, BMP_SIZE, BMP_SIZE, NULL, NULL, _hInst, NULL );
    }
 
    HINSTANCE _hInst;
    HWND      _hwnd;
    Ant       _ant;
};
//--------------------------------------------------------------------------------------------------
int APIENTRY _tWinMain( HINSTANCE hInstance, HINSTANCE hPrevInstance, LPTSTR lpCmdLine, int nCmdShow )
{
    wnd myWnd;
    return myWnd.Run( hInstance );
}
//--------------------------------------------------------------------------------------------------
 