Illusions
The R implementations for these are from Kohske Takahashi (@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)