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That's a quick tour of cyclic.coefs! It’s a simple tool for exploring the world of series and signals. Find the full vignette with all this code at the GitHub repo.
🔗: github.com/randomplayab...
#rstats

GitHub - randomplayables/cyclic.coefs: Explore Series with Periodic Coefficients

Explore Series with Periodic Coefficients. Contribute to randomplayables/cyclic.coefs development by creating an account on GitHub.

github.com

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randomplayables.bsky.social @randomplayables.bsky.social · 13d

The package fully supports complex numbers. A 16-point complex exponential replicates 4x across geometric decay, completing one unit circle rotation per cycle. The final complex dot product encodes both amplitude AND phase—the very essence of a Fourier coefficient!

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randomplayables.bsky.social @randomplayables.bsky.social · 13d

Pulse Train Sampling:
A 4-point pulse (25% duty cycle) replicated 8x across exponential decay creates a sample-and-hold effect. The pulse acts as a periodic sampler, creating a "sample-and-hold" effect where only 1 in every 4 points contributes to the sum.

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randomplayables.bsky.social @randomplayables.bsky.social · 13d

Signal Windowing: Apply an 8-point triangular window that replicates 4x across a 32-point exponentially growing signal. Each cycle smoothly weights the underlying signal, creating a repeating envelope effect.

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randomplayables.bsky.social @randomplayables.bsky.social · 13d

8 sine cycles across 64 Fibonacci numbers. #Fibonacci #DataViz

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randomplayables.bsky.social @randomplayables.bsky.social · 13d

The alternating harmonic series: ln(2) emerges from just a 2-point pattern replicated 50x across a harmonic series.

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randomplayables.bsky.social @randomplayables.bsky.social · 13d

The Basel Problem, where Sum(1/n²) = π²/6.

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randomplayables.bsky.social @randomplayables.bsky.social · 13d

Orthogonality. An 8-point sine wave is replicated 4x across a 32-point cosine wave. The running dot product (in green) shows how they cancel out. #math #rstats

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randomplayables.bsky.social @randomplayables.bsky.social · 13d

At its heart, cyclic.coefs in #rstats makes it easy to explore what happens when you build a series by tiling a short periodic sequence (f) across a longer base sequences (g).

🔗: github.com/randomplayab...

#math 🧵

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randomplayables.bsky.social @randomplayables.bsky.social · 14d

Check out www.mathartfun.com for #math, #art, and #fun!

MathArtFun.com home page

Online store and gallery of mathematical art. Browse topics including tessellations, polyhedra, fractals, knots, dice, anamorphic art, M. C. Escher, origami, and architecture. Books, puzzles, poster...

www.mathartfun.com

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randomplayables.bsky.social @randomplayables.bsky.social · 14d

I'm not as strong as I would like in the epsilon-delta department so I'm working through Black/Red's epsilon-deltathon to get some extra practice:

www.youtube.com/watch?v=Afrn...

#math

How to do epsilon-delta proofs (ultimate calculus guide)

YouTube video by blackpenredpen

www.youtube.com

randomplayables.bsky.social @randomplayables.bsky.social · 15d

I need patience for this. That games that gave me mathematical insights that I actually use are are all #rstats shiny games (dealing with mixed effects models and informative hypothesis testing). rpcompute will help put those R heavy games onto the platform.

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randomplayables.bsky.social @randomplayables.bsky.social · 16d

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randomplayables.bsky.social @randomplayables.bsky.social · 16d

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randomplayables.bsky.social @randomplayables.bsky.social · 16d

Visit randomplayables.com, sign-up, and submit your game today.

#math #games #code #data

randomplayables.com/submit-guide

3-step submission guide below👇👇👇

Random Playables

Turn math ponderings into citizen science games

randomplayables.com

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randomplayables.bsky.social @randomplayables.bsky.social · 17d

#games

randomplayables.bsky.social @randomplayables.bsky.social · 21d

Play Free Sets at www.randomplayables.com to explore sum free sets and other varieties of free sets.

#math #gaming #citizenscience

randomplayables.bsky.social @randomplayables.bsky.social · 22d

Diagram looking sick & dizzy at the moment. But we'll make it through.

Consider yourself lucky if you ever want to read up on a topic that Diego Assencio (dassencio.org/102) has blogged about!

#math #geometry