## Comment: Re:It's that twat with the upside down head again. (Score 5, Informative) 147

Some of the confusion is that the original description is defined recursively in a way that 'c' only shows up once, and the initial value is not c. z[i] = z[i-1]^2+c. But because z[0] is defined = 0, you can effectively rewrite the sequence in terms of just 'c' starting from the second. The downside is that at first it might LOOK at first glance like the previous term is being added, which is why I like the recursive form.

Also, by not starting from 0 you miss out on a cool connection: for a given fixed C, the graph of convergence for non-zero choices of z[0] over the complex plane gives you a Julia Set. With the neat property that Julia Sets from C inside the Mandelbrot set are fully connected and Julia Sets from C outside the Mandelbrot Set are sparse disconnected Cantor spaces.

Also, by not starting from 0 you miss out on a cool connection: for a given fixed C, the graph of convergence for non-zero choices of z[0] over the complex plane gives you a Julia Set. With the neat property that Julia Sets from C inside the Mandelbrot set are fully connected and Julia Sets from C outside the Mandelbrot Set are sparse disconnected Cantor spaces.