Recent content by emergentecon

With all due respect, whilst your advice is well intentioned and I do appreciate it, you entirely missed the point. Whilst it would be nice to have the luxury of time, to take the perfect approach to learning, this is not based in reality. At times, short-term goals take precedence. I'm...

Your point is entirely valid - I agree 100%. I am new to mathematics, going the self-taught route (sort of), but have an exam of sorts. My problem is I have not developed a natural intuition yet for how functions 'graph' so to speak - so wanted to find a way to approach the problems, without...

Wow thank you so much! The answer was staring me in the face - but your explanation made it clear! Apologies for the lax use of the word 'graph'.

I'm curious if there is a heuristic or method to determine the inner and outer radii as used in the Washer Method, WITHOUT needing to graph anything?

True, and in fact, they refer to it as a map from what I see . . .

For instance, from here: http://mathworld.wolfram.com/MandelbrotSet.html The term Mandelbrot set can also be applied to generalizations of "the" Mandelbrot set in which the function is replaced by some other function. In the above plot...

I'm curious though, why on this site, they make use of the f(z) approach in discussing the mandelbrot set? http://www.math.cornell.edu/~lipa/mec/lesson5.html

Ok thank you very much for the explanation . . .

Thanks!

I mis-stated my question, meant to say his equation, as opposed to the set. As I know, when he was asked about his work, he wrote down the equation as: z -> z^2 + c So was wondering if, in this context, z = z^2 + c or f(z) = z^2 + c as opposed to z(n+1) = z(n)^2 + c

When asked about his work, Mandelbrot wrote his equation as such: z -> z^2 + c Is it permissible to also write it as: z = z^2 + c and / or f(z) = z^2 + c

For instance, if I wanted to implement the recursion in Excel, I would in essence specify it as f(z) = z^2 + c The mandelbrot set is often 'summarised' as z = z^2 + c so why is it wrong to write f(z) = z^2 + c ?

I can't say this helps me much. Is it wrong to say that if you iterate the function f(z) = z^2 + c over the complex numbers, that you get the mandelbrot set?

Correct yes . . . under iteration, and z + c are complex numbers. Thanks!

f(z) = z2 + c