void TForm1::Draw()
			{
			    if ( bmp_valid )
			        return;
			        
			    Button1->Enabled = false;
			
			    const int maxiter = 100; // use 10000 for the other interval, commented below:
			    double minx, miny, maxx, maxy;
    			
			    minx = -2.2; maxx = 1.2;
			    miny = -1.4; maxy = 2.4;
			    // minx = 0.155206; maxx = 0.155207;
			    // miny = -0.650837; maxy = -0.650836;
    			
			    double cr, ci, zr, zi, zsq, tmp;
    			
			    cr = ci = 0.0;
    			
			    TCanvas *cnv = bmp->Canvas;
			    int      w   = PaintBox1->Width;
			    int      h   = PaintBox1->Height;
    			
			    for ( int i = 0; i < w; i++ ) {
			        for ( int j = 0; j < h; j++ ) {
			            cr = minx + i * ( maxx - minx ) / w;
			            ci = miny + j * ( maxy - miny ) / h;
			            int count = 0;
			            zr = 0.0;
			            zi = 0.0;
			            zsq = 0.0;
			            while ( (zsq < 4.0) && (count++ < maxiter) ) {
			                tmp = zr * zr - zi * zi;
			                zi = 2.0 * zr * zi + ci;
			                zr = tmp + cr;
			                zsq = zr * zr + zi * zi;
			            }
			            if ( count == maxiter ) {
			                cnv->Pixels[i][j] = clBlack;
			            } else {
	        		        cnv->Pixels[i][j] = 1 + count * maxiter; // RGB( count, count, count );
			            }
			        }
			        PaintBox1->Canvas->Draw( 0, 0, bmp );
			        Caption = "Column " + IntToStr( i );
			    }
			    bmp_valid = true;
			    Button1->Enabled = true;
			    
			} // end TForm1::Draw()