| | R
Defining recursive sine functions
(inelegantly)
> sin1 <- function(x)
+ { x0 <- sin(x); x1 <- sin(pi*x0); return(x1)}
> sin2 <- function(x)
+ { x0 <- sin(x); x1 <- sin(pi*x0); x2 <- sin(pi*x1); return(x2)}
> sin3 <- function(x)
+ { x0 <- sin(x); x1 <- sin(pi*x0); x2 <- sin(pi*x1); x3 <- sin(pi*x2); return(x3)}
(Timesing by π is to match the range of the output to the domain of the next input. Sin returns [-1,1] but reads in from [-π, π].)
Plotting them
par(mfrow=c(2,2)); plot(sin,-pi,pi); plot(sin1, -pi,pi); plot(sin2, -pi, pi); plot(sin3, -pi, pi)
One more trick
I want to see what sin50 would look like, or generally sin_i.
> sinai <- function(x, n)
+ {p <- sin(x); for(i in 1:n){ p <- sin(pi*p); i<- i+1} ; return(p)}
(p is the internal input/output of the recursive sines)
Now to print that...
> sin50 <- function(x) {return(sinai(x,50))}
> sin100 <- function(x) { return ( sinai (x, 100))}
> sin1000 <- function(x) {return( sinai (x, 1000))}
> sin10000 <- function(x) {return(sinai (x, 10000))}
> par(mfrow=c(2,2)); plot(sin50, -pi, pi); plot(sin100, -pi, pi); plot(sin1000, -pi, pi); plot(sin10000, -pi, pi)
And scene. |
| | Posted 7/10/2009 4:27 PM - 7 Views - 0 eProps - 0 comments
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