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[WSS20] Study of Shapes and Curves Defined by Curvature vs Arc Length

Posted 2 months ago
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Very nice exploration. I made a function on the WFR that does something similar.

https://resources.wolframcloud.com/FunctionRepository/resources/CurvaturePlot

Did you automate the classification, or manually? Very nice code and beautiful patterns. Thanks for sharing!

Thank you a lot!. Yes, it was sad to find your function -that was just what I needed- after I had done most of the work, mostly because the options that it offers would have been really helpful to allow further explorations.

The classification was manual with help from some Machine Learning functions like the FeactureSpacePlot function.

Thank you!

There is a bit of difference between your function and mine: Imagine sitting in a car and driving: Your 'instructions' to turning the steering wheel is based on the distance travelled (odometer) while mine is based on time (watch). So unless you're driving a constant speed the functions seem identical indeed.

I like the very intricate patterns the function generated even for relatively simple functions. Thanks again for sharing.

Hi, I was wondering the following:

Since arc length is usually defined for curves with a defined derivative, then, what would your code do with functions that have no derivative?

In particular, there are some functions that are continuous over the real line, but that are not differentiable at any point. Weierstrass function is an example of this:

https://mathworld.wolfram.com/WeierstrassFunction.html

I have tried your code, and Sander's code with this function, I am attaching the notebook below.

In short: Your code does, sometimes, plot something for this function, but I get a lot or Message errors about problems with the derivative. Of course, that makes sense given the properties of this function.

I also tried your code using the absolute value, that has a sharp corner, and with a steep step function.

It has been very fun, nice work!

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Great post Alejandra, Congratulations.

I noticed that you are interested in complex network analysis.

Presently I am studying complex network analysis for rainfall processes over different countries. May I ask my questions in this case via your email address? May I have your email address?

Take care and Kind regards

Mohammad

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