A question on the Mandelbrot set example- given X_i samped from Unif(S), how does one procedurally test whether X_i is a member of the Mandelbrot set or not?
same comment. i suggest you remove this Mandelbrot set fractal example since it has to be computed sequentially so can't be approximated using MC. it's confusing for the audience. but thanks for your lectures. they are all pretty nice and clear.
I like the Mandelbrot example, it's pretty cool. It took me maybe 10 minutes to code it in R: mandel = function(z0, nmax=200) { i = 0 z = z0 while((i=i+1) < nmax & Mod(z) < 2) z = z^2 + z0 return(i >= nmax) } N = 10000 Z = complex(real=runif(N,-2,2), imaginary=runif(N,-2,2)) M = sapply(Z, mandel) Estimates = cumsum(M) / seq_len(N) * 16
I also feel this series might be much better if some practical examples are given, and I also think if would be better if all notations are more clearly defined.
@@yuanyuan3056 I disagree. I watch these videos to get high-level overview of the concepts and ideas of these topics. If you want some rigorous definitions etc. there are plentiful of books covering this stuff over thousands of pages.
why not show test monte carlo on regular geometry in order to demonstrate its efficacy
A question on the Mandelbrot set example- given X_i samped from Unif(S), how does one procedurally test whether X_i is a member of the Mandelbrot set or not?
www.wolframalpha.com/examples/MandelbrotJuliaSets.html
hahah yeah, discretizing always goes with data sniffing :D
What is the software that you are using for writing?
same comment. i suggest you remove this Mandelbrot set fractal example since it has to be computed sequentially so can't be approximated using MC. it's confusing for the audience.
but thanks for your lectures. they are all pretty nice and clear.
any pointers to why it cannot be approximated using MC?
I like the Mandelbrot example, it's pretty cool. It took me maybe 10 minutes to code it in R:
mandel = function(z0, nmax=200) {
i = 0
z = z0
while((i=i+1) < nmax & Mod(z) < 2) z = z^2 + z0
return(i >= nmax)
}
N = 10000
Z = complex(real=runif(N,-2,2), imaginary=runif(N,-2,2))
M = sapply(Z, mandel)
Estimates = cumsum(M) / seq_len(N) * 16
I would recommend not to use the language "who knows"
I also feel this series might be much better if some practical examples are given, and I also think if would be better if all notations are more clearly defined.
@@yuanyuan3056 I disagree. I watch these videos to get high-level overview of the concepts and ideas of these topics. If you want some rigorous definitions etc. there are plentiful of books covering this stuff over thousands of pages.