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I want to programmatically create small, really simple flow charts like the one below:

flowchart

Source: https://commons.wikimedia.org/wiki/File:LampFlowchart.svg

What is a good open-source software choice to do this?

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The classic software for doing this is Graphviz and its "dot" language.

There are several language bindings available, for many programming languages, actually. Many apps are built on top of graphviz, see Wikipedia article.

There is a very comprehensive repository "Awesome Graphviz" with lots of graphviz related links.

Recently I came across DiagrammeR, but this requires substantial web development skills and full commitment to the modern R ecosystem (R + RStudio + htmlwidgets + JavaScript + d3.js + viz.js + mermaid.js).

But see 2-minute showcasing video on their homepage. It shows almost pure graphviz code (wrapped in a single R function). From simple graph to more complex graph, with animations and "hot reloading".

Previous related Qs about Graphviz and Alternatives

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You can use https://app.diagrams.net/ for free in your browser. It is easy to use!

Click on Create New Diagram and it lets you select from various flowchart templates:

flowchart models at diagrams.net

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