Good news! (or bad news)
You're implementation is completely. correct. Unfortunately, with c = [0, 1]
, the Julia set has very few points. I believe it is measure zero (unlike say, the Mandelbrot set). So the probability of a random point being in that Julia set is 0.
If you reduce your iterations to 15 (JSFiddle), you can see the fractal. One hundred iterations is more "accurate", but as the number of iterations increase, the chance that a point on your 400 x 400 grid will be included in your fractal approximation decreases to zero.
Often, you will see the Julia fractal will multiple colors, where the color indicates how quickly it diverges (or does not diverge at all), like in this Flash demonstration. This allows the Julia fractal to be somewhat visible even in cases like c = i.
Your choices are
(1) Reduce your # of iterations, possibly depending on c
.
(2) Increase the size of your sampling (and your canvas), possibly depending on c
.
(3) Color the points of your canvas according to the iteration # at which R
was exceeded.
The last option will give you the most robust result.