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Fractional Levy stable motion

December 28, 2021 Aleksejus Kononovicius #interactive #fractals #Brownian motion #topic: ARFIMA #Levy processes

The last post in the ARFIMA series was not the last stop in understanding the model we have studied in [1]. In the paper we have looked at ARFIMA as a model for fractional Levy stable motion (abbr. FLSM), which is a generalization of Brownian motion in two regards: fractionality and noise distribution.

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Numberphile: Chaotic Balls

December 21, 2021 Aleksejus Kononovicius #video #Numberphile #dynamical chaos #classical mechanics

In this Numberphile video Matt Henderson talks about creating animations illustrating chaos theory. In fact it is somewhat surprising that apparently simple linear system (bouncing ball) exhibits chaotic behavior. How? Watch the video below and find out.

ARFIMA(p, d, q) model

December 14, 2021 Aleksejus Kononovicius #interactive #fractals #Brownian motion #topic: ARFIMA #time series models

Slowly but surely we have finally reached ARFIMA model! Taking such small step (adding letter F to the acronym) took a lot of effort, but it was worth it. Why? Well, this exercise has allowed me to get a glimpse at fractional calculus and develop some intuition with this tool.

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Numerical fractional derivative

November 30, 2021 Aleksejus Kononovicius #interactive #1/f noise #fractals #methods #topic: ARFIMA #Python

Last time we have looked into fractional derivatives and even managed to derive fractional derivative for \( f(x) = x \). For more complicated functions this is much more problematic. Here, in this post, we will show you a quick numerical method to calculate fractional derivative of any arbitrary series.

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Tom Rocks Maths: Making mathematical art with L-systems

November 23, 2021 Aleksejus Kononovicius #video #fractals #L-system #Tom Rocks Maths

This video from Tom Rocks Maths Youtube channel talks about L-system. One can use L-system to artificially generate realistic botanical drawings. Fascinating isn't it?

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