nDimCubeAdjacency <- function(dim, steps = FALSE, self = FALSE)
{ adjacency       <- matrix(nrow = 2 ^ dim, ncol = 2 ^ dim)
  adjacency[1, 1] <- if ( self ) 1 else 0

  if ( dim )
  { for ( curDim in 1 : dim )
    { adjValue <- if ( steps ) curDim else 1
      width    <- 2 ^ curDim
      width2   <- width / 2

      adjacency[(width2 + 1) : width , (width2 + 1) : width ] <-
        sign(adjacency[1 : width2, 1 : width2]) * adjValue
      adjacency[(width2 + 1) : width , 1            : width2] <-
      adjacency[1            : width2, (width2 + 1) : width ] <-
        diag(adjValue, nrow = width2)
    }
  }

  return(adjacency)
}

plot.matrix.image <- function(matrix, colLevels = 2, emptyColor = 'white', col = NULL)
{ if ( is.null(col) )
  { col <- c(emptyColor
    , gray(seq(0, by = 1 / (colLevels - 1), length.out = colLevels - 1)))
    breaks <- 0 : colLevels - 0.5
  } else
    breaks <- 0 : length(col) - 0.5

  breaks[1]              <- min(matrix) - 0.5
  breaks[length(breaks)] <- max(matrix) + 0.5

  image(
    1 : ncol(matrix)
  , 1 : nrow(matrix)
  , t(matrix)
  , ylim = c(nrow(matrix) + 0.5, 0.5)
  , axes = FALSE, xlab = '', ylab = ''
  , col  = col
  , breaks = breaks
  )
  col <- 'lightgray'
  box(col = col)
  grid(ncol(matrix), nrow(matrix), lty = 'solid', col = col)
}

test.plot.matrix.image <- function(dim, steps = TRUE, self = FALSE, emptyColor = 'white', col = NULL)
{ plot.matrix.image(nDimCubeAdjacency(dim, steps = steps, self = self)
  , if ( steps && dim ) dim + 1 else 2, emptyColor, col = col)
}

adDimSeparators <- function(dim, col = 'red', lwd = 3, ...)
{ start <- 0.5
  end   <- 2 ^ (0 : (dim - 1)) + start

  segments(start, end, end, end  , col = col, lwd = lwd, ...)
  segments(end  , end, end, start, col = col, lwd = lwd, ...)
}

test.overall.plot.matrix.image <- function(cellWidth = 16)
{ dim       <- 4   ###### currently FIX, because of fixec color vector
  size      <- 2 ^ dim * cellWidth + 2
  png(filename = 'T:\\nDimCubeAdjacency.png', width = size, height = size)
  par <- par()
  par(mar = c(0, 0, 0, 0))
  test.plot.matrix.image(dim, col = (c('#0000C040', '#EFEFEF', '#A0A0A0', '#787878', 'black')))
  adDimSeparators(dim, lwd = 2)
  # adDimSeparators(dim)
  # adDimSeparators(dim, col = 'yellow', lwd = 1)
  dev.off()
}

edgesNDimCube <- function(dim)
{ return(
    if ( 0 == dim ) 0
    else 2 * edgesNDimCube(dim - 1) + 2 ^ (dim - 1)
    )
}

edges2cornerNDimCubeRatios <- function(dim)
{ return(sapply(0 : dim, edgesNDimCube) / 2 ^ (0 : dim)) }