0 like 0 dislike
0 like 0 dislike
Why does the Mandelbrot Set look the way it does? Is it possible for this set to have a different shape, such as an octagon?

2 Answers

0 like 0 dislike
0 like 0 dislike
The classical Mandelbrot set is for the function f(z)=z^(2)+c. Different functions give different shapes. E.g. for f(z)=z^(3)+c, the Mandelbrot set is symmetric left-to-right as well as top-to-bottom.
0 like 0 dislike
0 like 0 dislike
What do you mean?

The mandelbrot set is the set of all complex numbers c for which if we start at 0 and iterate the function f(z) = z^2 + c the sequence of numbers we get stays bounded. It is this one thing and it has the one definite shape we all know.

We can define lots of different sets in similar ways that can have all kinds of shapes, but those are not the mandelbrot set.

Related questions

0 like 0 dislike
0 like 0 dislike
1 answer
MSR_Tlse asked Jun 21
Are the S3/S4 Edexcel Further Maths units useful to become an actuary? Topics include sampling, unbiased and biased estimators, confidence intervals and significance test...
MSR_Tlse asked Jun 21
0 like 0 dislike
0 like 0 dislike
0 answers
kymdouglas asked Jun 21
Free version of Hardy, An Introduction to the Theory of Numbers
kymdouglas asked Jun 21
0 like 0 dislike
0 like 0 dislike
1 answer
MSimonTV asked Jun 21
Prereqs for An Introduction to the Theory of Numbers by GH Hardy?
MSimonTV asked Jun 21
0 like 0 dislike
0 like 0 dislike
3 answers
BlaiseJames asked Jun 21
#53. In the second part after "So, let delta = epsilon" how do they go from |-(x+5)|<E to |-(x-5)-10|<E? In the first part is there a name for the rule/property used to f...
BlaiseJames asked Jun 21
0 like 0 dislike
0 like 0 dislike
3 answers

24.8k questions

103k answers

0 comments

33.7k users

OhhAskMe is a math solving hub where high school and university students ask and answer loads of math questions, discuss the latest in math, and share their knowledge. It’s 100% free!