# Illusions

The R implementations for these are from Kohske Takahashi[(@kohske)](https://twitter.com/kohske). See http://rpubs.com/kohske/R-de-illusion from statmethods.net

## Cafe wall illusion

All the lines are actually parallel.

    library(grid)
    rs <- expand.grid(x = seq(0, 1, 1/10), y = seq(0, 1, 1/10))
    grid.rect(rs$x, rs$y, 1/10/2, 1/10/2, gp = gpar(fill = "black", col = NA))
    grid.rect(rs$x + 1/10/4, rs$y + 1/10/2, 1/10/2, 1/10/2, gp = gpar(fill = "black", col = NA))
    ls <- expand.grid(x = 0:1, y = seq(0, 1, 1/20) - 1/20/2)
    grid.polyline(ls$x, ls$y, id = gl(nrow(ls)/2, 2), gp = gpar(col = "grey50", lwd = 1))

## Ouchi

Move your frame of reference to see the effect.

    grid.newpage()
    nx <- 10; ny <- 30
    rs <- expand.grid(x = seq(0, 1, 1/nx/2), y = seq(0, 1, 1/ny/2))
    grid.rect(rs$x, rs$y, 1/nx/2, 1/ny/2, gp = gpar(col = NA, fill = c("black", "white")))
    rs <- expand.grid(x = seq(0.25, 0.75, 1/nx/2), y = seq(0.25, 0.75, 1/ny/2))
    grid.rect(rs$y, rs$x, 1/ny/2, 1/nx/2, gp = gpar(col = NA, fill = c("black", "white")))

## Fraser illusion

All the lines are actually parallel.

    library(plyr)
    grid.newpage()
    n <- 10; ny <- 8; L <- 0.01; c <- seq(0, 1, length = n); d <- 1.2*diff(c)[1]/2
    col <- c("black", "white")
    x <- c(c-d, c, c+d, c)
    y <- rep(c(0, -d, 0, d), each = n)
    w <- c(c-d, c-d+L, c+d, c+d-L)
    z <- c(0, L, 0, -L)
    ys <- seq(0, 1, length = ny)
    grid.rect(gp = gpar(fill = gray(0.5), col = NA))
    l_ply(1:ny, function(i) {n
      if (i%%2==0) {
        co <- rev(col)
        z <- -z
      } else {
        co <- col
      }
      grid.polygon(x, y + ys[i], id = rep(1:n, 4), gp = gpar(fill = co, col = NA))
      grid.polygon(w, rep(z, each = n) + ys[i], id = rep(1:n, 4), gp = gpar(fill = rev(co), col = NA))
    })

## Fraser-Wilcox illusion

    grid.newpage()
    No <- 3
    wo <- 1/3/2
    po <- seq(0, 1, by = wo)[(1:No) * 2]
    Nc <- 8
    tc <- seq(pi * 11/12, pi * 1/12, len = Nc)
    px <- c(outer(wo * cos(tc), po, `+`))
    wc <- rep(sin(tc), No)
    ag <- rep(1:No, each = Nc)
    dc <- 21
    th <- seq(0, 2 * pi, len = dc)
    grid.rect(gp = gpar(col = NA, fill = "#D2D200"))
    for (y0 in seq(0, 1, len = 10)) {
      for (i in seq_along(px)) {
        th <- seq(pi/2, pi/2 + 2 * pi, len = 21)
        if (ag[i]%%2==0) th <- rev(th)
        x <- px[i] + 0.5 * 0.04 * cos(th) * wc[i]
        y <- y0 + 0.04 * sin(th)
        grid.polygon(x, y, gp = gpar(fill = "#3278FE"))
        grid.polyline(x[1:((dc + 1)/2)], y[1:((dc + 1)/2)], gp = gpar(lineend = "butt", lwd = 3, col = gray(0)))
        grid.polyline(x[-(1:((dc - 1)/2))], y[-(1:((dc - 1)/2))], gp = gpar(lineend = "butt", lwd = 3, col = gray(1)))
      }
    }

## Parallel curves

These curves are the same offset apart for every x, even though it looks like they converge.

    x=1:100
    y=1/log10(x)
    y2=y+.2
    plot(x,y, type='l', ylim=c(0,1.5))
    lines(x,y2)