#
#
################################################################################
#

# The Lissajous Curve(s): http://en.wikipedia.org/wiki/Lissajous_curve

a <- 5 # Change this, but always bigger than "b".
b <- 2 # Change this, but always smaller than "a".
N <- 10
A <- 3 # Narrow or Wide.
B <- 3 # Tall or Short.
delta <- ((N - 1)/N) * (pi/2)
n <- 1000
t <- seq(1,n, by = 1)

x <- A * sin((a*t[1]) + delta)
y <- B * sin(b*t[1])
plot(x,y, col = "red", xlim = c(-3,3), ylim = c(-3,3))

for(i in 1:n){
  new.x <- A * sin((a*t[i]) + delta)
  new.y <- B * sin(b*t[i])
  par(new = T)
  plot(new.x,new.y, col = "blue", xlim = c(-3,3), ylim = c(-3,3))
  Sys.sleep(.01)
  if(i == n){print("DONE")}
 }

# Alternative forms: http://www.2dcurves.com/higher/higherli.html

# x <- sin(t)
# y <- sin((a*t) + b)

################################################################################

# Butterfly curve (transcendental)
# http://en.wikipedia.org/wiki/Butterfly_curve_%28transcendental%29

n <- 850
e <- 2.718281828
t <- seq(1:n)
x <- 0; y <- 0
plot(x, y, xlim = c(-4,4), ylim = c(-4,4), col = "red", pch = 1, xlab = "X", ylab = "Y")

for(i in 1:n){
  new.x <- sin(t[i]) * ((e^(cos(t[i]))) - 2*cos(4*t[i]))
  new.y <- cos(t[i]) * ((e^(cos(t[i]))) - 2*cos(4*t[i]))
  par(new = T)
  plot(new.x, new.y, xlim = c(-4,4), ylim = c(-4,4), col = "darkblue", pch = 1,
    xlab = "X", ylab = "Y")
  Sys.sleep(.01)
  if(i == n){print("DONE")}
}

################################

# Somewhat the reverse of what was just done above.

n <- 850
e <- 2.718281828
t <- seq(1:n)
x <- 0; y <- 0
plot(x, y, xlim = c(-4,4), ylim = c(-4,4), col = "red", pch = 1, xlab = "X", ylab = "Y")

for(i in 1:n){
  new.x <- sin(t[i]) * ((e^(cos(t[i]))) - 2*cos(4*t[i]) - ((sin(5))*(t/12)))
  new.y <- cos(t[i]) * ((e^(cos(t[i]))) - 2*cos(4*t[i]) - ((sin(5))*(t/12)))
  par(new = T)
  plot(new.x, new.y, xlim = c(-4,4), ylim = c(-4,4), col = "darkblue", pch = ".",
    xlab = "X", ylab = "Y")
  Sys.sleep(.01)
  if(i == n){print("DONE")}
}

################################

# Another slight variation.

n <- 850
e <- 2.718281828
t <- seq(1:n)
x <- 0; y <- 0
plot(x, y, xlim = c(-4,4), ylim = c(-4,4), col = "red", pch = 1, xlab = "X", ylab = "Y")

for(i in 1:n){
  new.x <- sin(t[i]) * ((e^(cos(t[i]))) - 2*cos(4*t[i]) + ((sin(5))*(t/12)))
  new.y <- cos(t[i]) * ((e^(cos(t[i]))) - 2*cos(4*t[i]) + ((sin(5))*(t/12)))
  par(new = T)
  plot(new.x, new.y, xlim = c(-4,4), ylim = c(-4,4), col = "darkblue", pch = ".",
    xlab = "X", ylab = "Y")
  Sys.sleep(.01)
  if(i == n){print("DONE")}
}

################################

# Multi-colored, with some variation from applying weights.

n <- 7000
e <- 2.718281828
t <- seq(1:n)
v <- c(2,3,4)
my.col <- c("blue","lightblue","lightgreen","darkgreen","darkblue")
x <- 0; y <- 0
plot(x, y, xlim = c(-5,5), ylim = c(-6,6), col = "red", pch = 1, xlab = "X", ylab = "Y")

for(i in 1:n){
  w <- sample(v, 1)
  new.x <- sin(t[i]) * ((e^(cos(t[i]))) - w*cos(4*t[i]))
  new.y <- cos(t[i]) * ((e^(cos(t[i]))) - w*cos(4*t[i]))
  par(new = T)
  plot(new.x, new.y, xlim = c(-5,5), ylim = c(-6,6), col = sample(my.col, 1), pch = 1,
    xlab = "X", ylab = "Y")
  if(i == n){print("DONE")}
}

################################

# Another slight variation.

n <- 7000
e <- 2.718281828
t <- seq(1:n)
v <- c(2,3,4)
x <- 0; y <- 0
plot(x, y, xlim = c(-4,4), ylim = c(-4,4), col = "red", pch = 1, xlab = "X", ylab = "Y")

for(i in 1:n){
  m <- sample(v, 1)
  new.x <- sin(t[i]) * ((e^(cos(t[i]))) - 2*cos(m*t[i]))
  new.y <- cos(t[i]) * ((e^(cos(t[i]))) - 2*cos(m*t[i]))
  par(new = T)
  plot(new.x, new.y, xlim = c(-4,4), ylim = c(-4,4), col = "blue", pch = ".",
    xlab = "X", ylab = "Y")
  if(i == n){print("DONE")}
}

################################

# Alternative...

n <- 800
e <- 2.718281828
t <- seq(1:n)
x <- 0; y <- 0
plot(x, y, xlim = c(-4,4), ylim = c(-4,4), col = "red", pch = 1, xlab = "X", ylab = "Y")

for(i in 1:n){
  new.x <- sin(t[i]) * ((e^(cos(t[i]))) - 2*cos(4*t[i]) - ((sin(1)^5)*(t/12)))
  new.y <- cos(t[i]) * ((e^(cos(t[i]))) - 2*cos(4*t[i]) - ((sin(1)^5)*(t/12)))
  par(new = T)
  plot(new.x, new.y, xlim = c(-4,4), ylim = c(-4,4), col = "darkblue", pch = ".",
    xlab = "X", ylab = "Y")
  Sys.sleep(.05)
  if(i == n){print("DONE")}
}

################################

#  From: http://paulbourke.net/geometry/butterfly/
# x = cos(u) (ecos(u) - 2 cos(4 u) - sin(u / 12)5.0)  --> Here, 'u' is theta, or 't' below.
# y = sin(u) (ecos(u) - 2 cos(4 u) - sin(u / 12)5.0)

n <- 3000
x.vec <- as.vector(0)
y.vec <- as.vector(0)
e <- 2.718281828
t <- seq(1,n)
for(i in 1:n){
 x <- cos(t[i]) * ((e^(cos(t[i]))) - (2*cos(4*t[i])) - (sin(t[i]/12)^5))
 y <- sin(t[i]) * ((e^(cos(t[i]))) - (2*cos(4*t[i])) - (sin(t[i]/12)^5))
 x.vec[i] <- y
 y.vec[i] <- x
 }
plot(x.vec,y.vec, col = "darkgreen")

################################
################################

# And finally, this is what the Butterfly is supposed to look like.
# Note: this takes a minute or so.

n <- 15000
e <- 2.718281828
t <- seq(1:n)
my.col <- c("blue","lightblue","lightgreen","darkgreen","darkblue")
x <- 0; y <- 0
plot(x, y, xlim = c(-4,4), ylim = c(-3,4), col = "red", pch = 1, xlab = "X", ylab = "Y")

for(i in 1:n){
 new.x <- cos(t[i]) * ((e^(cos(t[i]))) - (2*cos(4*t[i])) - (sin(t[i]/12)^5))
 new.y <- sin(t[i]) * ((e^(cos(t[i]))) - (2*cos(4*t[i])) - (sin(t[i]/12)^5))
 par(new = T)
 plot(new.y, new.x, xlim = c(-4,4), ylim = c(-3,4), col = sample(my.col, 1), pch = ".",
   xlab = "X", ylab = "Y")
 if(i == n){print("DONE")}
 }

# Larger points; more pronounced.

n <- 15000
e <- 2.718281828
t <- seq(1:n)
my.col <- c("blue","lightblue","lightgreen","darkgreen","darkblue")
x <- 0; y <- 0
plot(x, y, xlim = c(-4,4), ylim = c(-3,4), col = "red", pch = 1, xlab = "X", ylab = "Y")

for(i in 1:n){
 new.x <- cos(t[i]) * ((e^(cos(t[i]))) - (2*cos(4*t[i])) - (sin(t[i]/12)^5))
 new.y <- sin(t[i]) * ((e^(cos(t[i]))) - (2*cos(4*t[i])) - (sin(t[i]/12)^5))
 par(new = T)
 plot(new.y, new.x, xlim = c(-4,4), ylim = c(-3,4), col = sample(my.col, 1), pch = 1,
   xlab = "X", ylab = "Y")
 if(i == n){print("DONE")}
 }

################################################################################

# Torus:
# http://en.wikipedia.org/wiki/Parametric_equation
# See the "Parametric Surfaces" section.

# Torus with major radius R and minor radius r may be defined parametrically as
# x = cos(t)*(R + (r*cos(u)))
# y = sin(t)*(R + (r*cos(u)))
# z = r*sin(u)
# where the two parameters t and u both vary between 0 and 2*pi.

# Example 1: Not a Torus, but still interesting.

library(scatterplot3d)

n <- 63
x.fun <- function(t,R,r){x <- cos(t)*(R + (r*cos(u))); return(x)}
y.fun <- function(t,R,r){y <- sin(t)*(R + (r*cos(u))); return(y)}
z.fun <- function(r,u){z <- rep(r*sin(u),n); return(z)}

R <- 2
r <- 1/2

t <- seq(0, 2*pi, by = 0.1)
u <- seq(0, 2*pi, by = 0.1)

x <- 0; y <- 0; z <- 0
scatterplot3d(x, y, z, highlight.3d = TRUE, xlab = "x", ylab = "y", zlab = "z", type = "p",
   col.axis = "blue", angle = 55, col.grid = "lightblue", scale.y = 0.7, pch = 1,
   xlim = c(-3, 3), ylim = c(-3, 3), zlim = c(-3, 3))

for(i in 1:n){
  new.x <- x.fun(t[i], R, r)
  new.y <- y.fun(t[i], R, r)
  new.z <- z.fun(r, u[i])
  par(new = T)
  scatterplot3d(new.x, new.y, new.z, highlight.3d = TRUE, xlab = "x", ylab = "y",
    zlab = "z", type = "p", col.axis = "blue", angle = 55, col.grid = "lightblue",
    scale.y = 0.7, pch = ".", xlim = c(-3, 3), ylim = c(-3, 3), zlim = c(-3, 3))
  Sys.sleep(.25)
  if(i == n){print("DONE")}
}

################################

# Example 2: Torus.

library(scatterplot3d)

n <- 10000
x.fun <- function(t,R,r){x <- cos(t)*(R + (r*cos(u))); return(x)}
y.fun <- function(t,R,r){y <- sin(t)*(R + (r*cos(u))); return(y)}
z.fun <- function(r,u){z <- r*sin(u); return(z)}

R <- 2
r <- 1/2

TT <- seq(0, 2*pi, by = 0.1)
U <- seq(0, 2*pi, by = 0.1)

x <- 0; y <- 0; z <- 0
scatterplot3d(x, y, z, highlight.3d = TRUE, xlab = "x", ylab = "y", zlab = "z", type = "p",
   col.axis = "blue", angle = 55, col.grid = "lightblue", scale.y = 0.7, pch = 1,
   xlim = c(-3, 3), ylim = c(-3, 3), zlim = c(-3, 3))

for(i in 1:n){
  t <- sample(TT, 1)
  u <- sample(U, 1)
  new.x <- x.fun(t, R, r)
  new.y <- y.fun(t, R, r)
  new.z <- z.fun(r, u)
  par(new = T)
  scatterplot3d(new.x, new.y, new.z, highlight.3d = TRUE, xlab = "x", ylab = "y",
    zlab = "z", type = "p", col.axis = "blue", angle = 55, col.grid = "lightblue",
    scale.y = 0.7, pch = ".", xlim = c(-3, 3), ylim = c(-3, 3), zlim = c(-3, 3))
  if(i == n){print("DONE")}
}

################################################################################
<<<
##################### Mr. Fibbles' random wibbles. #############################
>>>
################################################################################

# "Can you get to a phone?"

library(RColorBrewer)

my.col <- brewer.pal(09, "Greens")
my.col <- my.col[9:2]
n <- 50
x <- seq(1, n, by = 1)
y <- seq(1, n, by = 1)
grid <- matrix(sample(c(letters,seq(1:9)), n^2, replace = T), nrow = n, ncol = n)
grid.n <- nrow(grid) * ncol(grid)
par(bg = "#002200")
plot(x, y, xlab = " ", ylab = " ", main = "The Matrix", col.main = my.col[8],
  xlim = c(1,n), ylim = c(1,n), col = "#003300")
for(j in 1:10){
 new.x <- 1
 new.y <- n + 1
 for(i in 1:grid.n){
   new.y <- new.y - 1
     if(new.y == 0){new.y <- n; new.x <- new.x + 1; if(j > 1){new.x <- sample(n, 1)}}
   par(new = T)
   plot(new.x, new.y, xlab = " ", ylab = " ", main = "The Matrix", col.main = my.col[8],
     xlim = c(1,n), ylim = c(1,n),col = sample(my.col, 1), pch = grid[new.x,new.y])
 }
 rm(i, new.x, new.y)
}





# End; Dec. 2, 2011.