AniWiki: Animations in Statistics

Gregor Gorjanc (PhD student), University of Ljubljana. 2007/11/12

ani.options(...)
ani.start(...)
for (i in 1:nmax) plot(...)
ani.stop()

# create an HTML animation page of Brownian Motion
# store the old option to restore it later
oopt = ani.options(interval = 0.05, nmax = 100, ani.dev = png, ani.type = "png",
    title = "Demonstration of Brownian Motion",
    description = "Random walk on the 2D plane: for each point (x, y), 
    x = x + rnorm(1) and y = y + rnorm(1).")
ani.start()
opar = par(mar = c(3, 3, 1, 0.5), mgp = c(2, .5, 0), tcl = -0.3,
    cex.axis = 0.8, cex.lab = 0.8, cex.main = 1)
brownian.motion(pch = 21, cex = 5, col = "red", bg = "yellow")
par(opar)
ani.stop()
ani.options(oopt)
y = 0.1 + runif(20, 0.2, 1)
xx = c(1, 1:20, 20)
yy = c(0, y, 0)
cl = seq(255, 0, length = 50)
for (i in 1:50) {
    yy = rbind(yy, c(0, y - (1 - cl[i]/255) * min(y), 0))
    plot(xx, yy[1, ], type = "n", xlab = "x", ylab = "y")
    for (j in 1:i) polygon(xx, yy[j + 1, ], col = rgb(1, cl[j]/255,
        0), border = NA\)
    Sys.sleep(0.1)
}
oopt = ani.options(interval = 0.2, nmax = 50, ani.dev = png, ani.type = "png",
    ani.height = 350, ani.width = 500,
    title = "Demonstration of Polygons with Gradient Colors",
    description = "The graph actually consists of a series of polygons, 
    each with a redder color starting from yellow.")
ani.start()
opar = par(mar = c(3, 3, 1, 0.5), mgp = c(2, .5, 0), tcl = -0.3,
    cex.axis = 0.8, cex.lab = 0.8, cex.main = 1)
 
####################
y = 0.1 + runif(20, 0.2, 1)
xx = c(1, 1:20, 20)
yy = c(0, y, 0)
cl = seq(255, 0, length = 50)
for (i in 1:50) {
    yy = rbind(yy, c(0, y - (1 - cl[i]/255) * min(y), 0))
    plot(xx, yy[1, ], type = "n", xlab = "x", ylab = "y")
    for (j in 1:i) polygon(xx, yy[j + 1, ], col = rgb(1, cl[j]/255,
        0), border = NA\)
#    Sys.sleep(0.1)
#    not need to 'sleep' here!
}
 
####################
par(opar)
ani.stop()
ani.options(oopt)
library(Cairo)
library(animation)
oopt = ani.options(interval = 0.05, nmax = 100, ani.dev = CairoPNG, 
    title = "Demonstration of Brownian Motion", 
    description = "Random walk on the 2D plane")
ani.start()
opar = par(mar = c(3, 3, 1, 0.5), mgp = c(2, 0.5, 
    0), tcl = -0.3, cex.axis = 0.8, cex.lab = 0.8, cex.main = 1)
brownian.motion(pch = 21, cex = 5, col = "red", bg = "yellow")
par(opar)
ani.stop()
ani.options(oopt)
library(animation)
ani.options(interval = 0.3, ani.height = 450, ani.width = 600, 
    title = "Demonstration of Least Squares (Slope)", 
    description = "We want to find an estimate for the slope
                   in 50 candidate slopes, so we just compute the RSS one by one. ")
ani.start()
par(mar = c(4, 4, 0.5, 0.1), mgp = c(2, 0.5, 0), tcl = -0.3)
## slope changing
least.squares()
ani.stop()
 
## or with intercept changing
ani.options(interval = 0.3, ani.height = 450, ani.width = 600, 
    title = "Demonstration of Least Squares (Intercept)", 
    description = "We want to find an estimate for the intercept
                   in 50 candidate intercetps, so we just compute the RSS one by one. ")
ani.start()
par(mar = c(4, 4, 0.5, 0.1), mgp = c(2, 0.5, 0), tcl = -0.3)
# slope changing
least.squares(ani.type = "intercept")
ani.stop()
# create an HTML animation page of Brownian Motion
# store the old option to restore it later
oopt = ani.options(interval = 0.05, nmax = 100, ani.dev = png, ani.type = "png",
    title = "Demonstration of Brownian Motion",
    description = "Random walk on the 2D plane: for each point (x, y), 
    x = x + rnorm(1) and y = y + rnorm(1).")
ani.start()
opar = par(mar = c(3, 3, 1, 0.5), mgp = c(2, .5, 0), tcl = -0.3,
    cex.axis = 0.8, cex.lab = 0.8, cex.main = 1)
brownian.motion(pch = 21, cex = 5, col = "red", bg = "yellow")
par(opar)
ani.stop()
ani.options(oopt)
library(animation)
library(lattice)
bm.mat = data.frame(x = rnorm(10), y = rnorm(10))
oopt = ani.options(interval = 0.05, nmax = 100, ani.dev = png, ani.type = "png",
    title = "Demonstration of Brownian Motion",
    description = "Random walk on the 2D plane: for each point (x, y), 
    x = x + rnorm(1) and y = y + rnorm(1).")
## Brownian Motion in lattice
for (i in 1:ani.options("nmax")) {
    print(xyplot(y ~ x, bm.mat, xlim = c(-10, 10), ylim = c(-10, 
        10), pch = 19))
    bm.mat = bm.mat + data.frame(x = rnorm(10), y = rnorm(10))
}
ani.stop() 
ani.options(oopt)

topic	description	preview
Simulation of flipping coins	specify the true probability of the occurrence of each face, and do the simulation of flipping an object.
Brownian Motion	a trivial demonstration of the Brownian Motion; you can see some circles moving randomly on the 2D plane.
Buffon's Needle	present the scenario of dropping needles and estimate the value of .
Bean Machine	The bean machine, also known as the quincunx or Galton box, is a device invented by Sir Francis Galton to demonstrate the law of error and the normal distribution.
The Law of Large Numbers	as the sample size grows, the sample mean will converge to the population mean.
Central Limit Theorem	as the sample size grows, the distribution of the sample mean will converge to the Normal distribution; a histogram will illustrate the density of the sample mean and the Shapiro's test will be performed to check the normality (P-values will be plotted).

AniWiki: Animations in Statistics

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