Talk:Multifractal system

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Article needs expanding

In my opinion, the article needs to be expanded. A non-technical introduction may be very useful, as well as some external references.

Regarding the mathematical content, the presentation through singularity exponents makes it clearer than its alternatives (moments of partition functions or measures), although some relation to (turbulent) cascade models could be apropriate.

The only problem is an article about singularity exponents doesnt exist Lbertolotti —Preceding unsigned comment added by Lbertolotti (talk • contribs) 07:03, 10 April 2009 (UTC)[reply]

unassessed: http://www.physics.mcgill.ca/~gang/multifrac/index.htm - "multifractal explorer" created by a researcher featured by the New Scientist. --188.46.8.132 (talk) 12:20, 6 November 2009 (UTC)[reply]

This third sentence of the second paragraph has a comma in it that's confusing the heck out of me. Now, I'm already confused by the subject matter, so I might just be confused all around, but it just doesn't seem like English. "The origin of multifractality in sequential (time series) data has been attributed, to mathematical convergence effects related to the central limit theorem that have as foci of convergence the family of statistical distributions known as the Tweedie exponential dispersion models[2] as well as the geometric Tweedie models." Shouldn't that be comma free? 204.128.192.31 (talk) 18:21, 16 July 2014 (UTC)[reply]

Comma removed. Alsee (talk) 17:18, 8 March 2015 (UTC)[reply]

link to reference

In the "Estimation" section, the link to Roberts & Cronin 1996 doesn't work as it should, but I don't know how to fix it. Bubba73 ^{You talkin' to me?} 01:47, 18 November 2019 (UTC)[reply]

When I click on the link, I'm taken to a page that displays the message "Due to a server upgrade in July 2014, this web service is not working at the moment. Contact me by email." So, I regard the link as working, even though it doesn't lead to the work cited; but it looks like something a Wikipedia editor can't fix on their own, unless they can point it to another site. Dhtwiki (talk) 18:21, 19 November 2019 (UTC)[reply]

Heavy sentence exploded

Here's a somewhat definitional sentence from lead, reformatted with bullets:

The origin of multifractality in sequential (time series) data has been attributed to

mathematical convergence effects

related to the central limit theorem

that have as foci of convergence

the family of statistical distributions known as the Tweedie exponential dispersion models

as well as the geometric Tweedie models.

That's a bit too much to chew in one mouthful, is it not? — MaxEnt 02:17, 5 October 2022 (UTC)[reply]

The Definition section is not mathematically self-contained and is ambiguous/unclear

The article begins with a definition section that is not mathematically self-contained and is ambiguous/unclear. The only citation provided is a textbook, which will be difficult or impossible for users on certain devices to obtain for reference. Other places where references might be able to clarify the ambiguous notation lead to article stubs or say "citation needed".

The object $s$ is not well defined. Is it a set? Scalar-valued potential? Vector-valued field? Some other formal mathematical object? The reader can infer only that $s$ appears to admit what is (probably) a Euclidean vector space either as an index set or function argument, that it is an object for which the "scales as" relation $\sim$ is well-defined for $a^{h({\vec {x}})}$ , and that subtraction is well-defined on $s$ . This hints that $s$ is likely a vector of some sort.
The role of ${\vec {x}}$ and ${\vec {x}}+{\vec {a}}$ is unclear. If $s$ is a set, then this might a Euclidean vector spaces that indexes $s$ .
The exponent on the right-hand side $a^{h({\vec {x}})}$ is strange. We can expect reasonably intuitive definitions when the exponent is a real or complex scalar, and when the base is a scalar or a square matrix. However, the left-hand side tells us that ${\vec {a}}$ is some sort of vector. This leads me to suspect that $h({\vec {x}})$ must be a scalar, and that the exponent should be interpreted as acting elementwise on ${\vec {a}}$ . I suspect this cannot be correct, however.
My suspicion is that both the left and right sides of this similarity relation need to be wrapped in some sort of norm (which reduces both of them to a scalar). But, without working citations and referencing to the material this equation comes from, I cannot verify this. — Preceding unsigned comment added by 2A00:23C6:54A6:C901:F92:21CE:7DC6:5669 (talk) 09:35, 25 May 2025 (UTC)[reply]