In a 2015 presentation "Operadics: the mathematics of modular design", David Spivak describes operadics as "a sub-discipline of category theory (CT)."
Matriarch is "a high-level language of materials architecture, implemented in an open-source Python library."
Figure 2 in the paper Matriarch: A Python Library for Materials Architecture by Tristan Giesa, Ravi Jagadeesan, David I. Spivak, and Markus J. Buehler describes a simple operad called the little 2-cubes operad E₂. In my attempts to learn about category theory and operadics, I am trying to replicate this operad using Xholon and eTrice, both based on the ROOM formalism.
I have implemented part of the first Matriarch model in the paper.
The source code at github.
The source code as an editable and executable Xholon workbook.
The Xholon executable. It generates a chain of 30 amino acid names in Application > Model > CompositeStructureHierarchy > chameleon > physicalSystem > Your first Matriarch program:matriarch > myLongChain:attachSeries.
As a next step with Matriach, I have used brython to compile the Matriarch Python source code into JavaScript. The compiled JavaScript runs in the browser, but it fails during the chain() method for a reason that I don't yet understand. My goal is to run code that can be controlled by a Xholon nested structure (the logical/topological structure), that will generate the geometry and include the PDB data. My initial work on this is not yet available online.
Once this is working, I would then use PV - JavaScript Protein Viewer to display the proteins in the browser.
I have also built a Xholon implementation of Peter's "Manage Repository" model, specified as an Arrangement diagram and multiple Data Flow Diagrams (DFDs). My intention here is to demonstrate a larger nested system that seems to include both building instructions and building blocks. It's a hierarchical structure, with links (data flows) between processes and data stores.
The source code includes various explanations and links to other material. In addition to the Xholon workbook, this page includes several Graphviz and Mind Map exports as (hopefully) viewable SVG files.
The source code as an editable and executable Xholon workbook.
The Xholon executable. I exported the running model to several different formats. I obtained the clearest visualization by exporting it as a Mind Map .mm file, importing that into FreeMind or FreePlane, and then having that tool export it as a SVG image.
Several years ago I explored the structure of food recipes. I believe that this is operadic.
source code at github
source code as an editable Xholon workbook
Xholon executable with a Mind Map SVG visualization
MathML has an interesting structure.
source code at github
source code as an editable Xholon workbook
Xholon executable with a Mind Map SVG visualization
Spivak, 2013, THE OPERAD OF WIRING DIAGRAMS: FORMALIZING A GRAPHICAL LANGUAGE FOR DATABASES, RECURSION, AND PLUG-AND-PLAY CIRCUITS
source code at github
source code as an editable Xholon workbook
Rupel and Spivak, 2013, THE OPERAD OF TEMPORAL WIRING DIAGRAMS: FORMALIZING A GRAPHICAL LANGUAGE FOR DISCRETE-TIME PROCESSES
source code at github
source code as an editable Xholon workbook
I am building an IDE for the Operadics Domain Specific Language (DSL).
You can try it here.
Xholon GWT is a Xholon project. Copyright (C) 2017 Ken Webb
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