Polynomial knots in R

Question

This question is about a possible way to graphically represent knot polynomials as given by expressions here and here in R.

Unfortunately I didn`t get very far since my math knowledge is not so good. This is what I have tried

phi <- seq(-30, 30, len=1001) 
fx <- phi^5 - 28*phi  #these are the polynomials from the website above
fy <- phi^7 - 32*phi^3

which gives, when using plot(fx,fy)

and I guess it should have given the figure-eight-knot. I can find zeroes of the above functions over the specified interval, and it all seems ok,since both functions have pairs of very similar zero values as can be seen in the knot diagram. Any ideas?

Answer 1

Your code is correct. You just need to zoom in:

phi <- seq(-2.6, 2.6, len=1e5) 
fx <- phi^5 - 28*phi  
fy <- phi^7 - 32*phi^3

plot(fx, fy, type="l")

Answer 2

Try:

phi <- seq(-3, 3, len=1001) 
fx <- phi^5 - 28*phi  
fy <- phi^7 - 32*phi^3
plot(fx,fy,xlim=c(-50,50),ylim=c(-150,150))

You have to adjust the limits of your axis. HF