#asymptote — Public Fediverse posts

#SciArtSeptember day 5: ‘Orbit’

It is well-known that the three-body problem does not have a general closed-form analytic solution. But there are many known periodic solutions of varying complexity. So I offer the attached ‘artistic’ plot of twelve of these periodic solutions, produced using a small Python program and the #Asymptote graphics language.

PNG attached. For the same image in vector format (SVG+PDF): https://ajcain.codeberg.page/posts/2026-09-05-three-body-periodic-solutions.html

(The image was used as an illustration at the start of the main text of my book ‘Form & Number: A History of Mathematical Beauty’ [https://archive.org/details/cain_formandnumber_ebook_large].)

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#SciArt #periodicity

The #Mathober day 6 prompt is ‘Partial sum’, and so I offer a diagram of the #Fractal ‘blancmange curve’ or ‘Takagi curve’ and some of the partial sums that converge to it. It is defined on the unit interval by
\[
y(x) = \sum_{n=0}^\infty \frac{s(2^n x)}{2^n},
\]
where
\[
s(x) = \min_{n \in \mathbb{Z}}|x - n|.
\]
(See the Wikipedia article: https://en.wikipedia.org/wiki/Blancmange_curve)

In the diagram, successive partial sums are shown in darkening shades of grey and (an approximation to) the curve itself in black.

A vector version of the diagram in PDF format: https://ajcain.codeberg.page/posts/files/blancmange-curve.pdf

The #Asymptote source code (not particularly efficient) for the diagram: https://ajcain.codeberg.page/posts/files/blancmange-curve.asy

[Images released under the Creative Commons BY-SA 4.0 International Licence; code under the GPL 3.0.]

#Mathober2025

You can't be "free". No matter what, your environment and the people around you will impact your available choices. The question is can we be less negatively impacted and limited by the physical world, and can we find compromises with others to maximize everybody's experience in this limited lifespan.

Or can you somehow dominate such that the trade-offs are almost always nearly 100% in your favor. I guess that's what the never fucking done billionaires are trying to do. #asymptote

The more you scroll, the longer the document becomes. Scroll infinitely close to infinity:
https://asymptote.stewartsmith.io

#Infinity #Asymptote #Art #WebArt #Minimalism

There are two things that always fascinated me. One, the graphics language developed in #MetaFont → #MetaPost → #asymptote And second, connecting various libraries from different sources.

With that in mind, here's another proof of concept of an interface for loading asymptote paths expressions into #CadQuery.

🆕 The pandoc #filter "diagram" generates images from text definitions. Currently supported: #TikZ, #Asymptote, #GraphViz, #Mermaid, and #PlantUML.
#Quarto users can install the filter with
quarto add pandoc-ext/diagram

https://github.com/pandoc-ext/diagram

@aka_quant_noir @CharJTF

Ding ding! Ya'll are so smart!

#Asymptote #Graph