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[parent] Viewing Correction to 'Mandelbrot set'
Iterated function, Julia sets by Koro

Correction id: 11777
Filed on: 2007-04-22 13:25:16
Status: Accepted on 2007-04-26 17:51:55
Type: Erratum

Correction text:
1) The phrase "The Mandelbrot set is a map on the complex plane of all possible Julia sets" doesn't sound like it makes much sense. A set that is a map? And it is a map of sets? Would you please change it/clarify it?

2) Maybe you should be a bit more specific in the statement of the definition of the mandelbrot set: "defined as the set of points c where the sequence 0, f_c(0), f_c(f_c(0))... is bounded" or something alike (you should at least mention the initial value, btw)

Comment from object owner PrimeFan:
2) Maybe you should be a bit more specific in the statement of the definition of the mandelbrot set: "defined as the set of points c where the sequence 0, f_c(0), f_c(f_c(0))... is bounded" or something alike (you should at least mention the initial value, btw)


The initial value is 0 only at the point 0 + 0i. At -1 + 0i (the center of the left cardioid) the function's first input value is that value -1 + 0i.


1) The phrase "The Mandelbrot set is a map on the complex plane of all possible Julia sets" doesn't sound like it makes much sense. A set that is a map? And it is a map of sets? Would you please change it/clarify it?


It is pretty clear to anyone who has played around with FractInt's Mandelbrot-to-Julia, where you click on a point in the Mandelbrot set and it shows you the corresponding Julia set. I'll move the paragraph that mentions that up, I suppose it will still confuse the most literal-minded machines.
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About the correction for Mandelbrot set by Koro on 2007-04-26 18:23:33
>2) Maybe you should be a bit more specific in the statement of the
>definition of the mandelbrot set: "defined as the set of points c
>where the sequence 0, f_c(0), f_c(f_c(0))... is bounded" or something
>alike (you should at least mention the initial value, btw)


>>The initial value is 0 only at the point 0 + 0i. At -1 + 0i (the
>>center of the left cardioid) the function's first input value is
>> that value -1 + 0i.

Well that is not stated in the definition. If you are defining something recursively you should state what the first value is.
You may just say you take the initial value to be 0, since it gives the same set (the next value will be c, as you wanted).

>>1) The phrase "The Mandelbrot set is a map on the complex plane of
>>all possible Julia sets" doesn't sound like it makes much sense. A
>>set that is a map? And it is a map of sets? Would you please change
>>it/clarify it?


>It is pretty clear to anyone who has played around with FractInt's
>Mandelbrot-to-Julia, where you click on a point in the Mandelbrot set
>and it shows you the corresponding Julia set. I'll move the paragraph
>that mentions that up, I suppose it will still confuse the most
>literal-minded machines.

You're taking for granted that anyone who reads this entry has used fractint before? But even in that case, I have used fractint before, and I mantain my objection to the first phrase of this definition: it makes no sense. The mandelbrot set is not a map of julia sets. It's not even a map. It's a set.
I'm sure you're trying to say something meaningful in that sentence, but you should seriously try to say it in a different way.

Is it asking too much if I request that you add a correct definition of the mandelbrot set in the first paragraph? It's not like it will use obscure terms or fancy math symbols. You just have to say that
the mandelbrot set is the *set* of all c's such that the *sequence defined by iterating f_c* (starting at 0, or c) remains bounded.

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