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Examples [accessible -- no dynamic graphics]#

Table of Contents#

Illustratory Models#

Iterable Models#

Using Models as live in-the-loop digital twins, creating your own model pipelines, and streaming simulation results to update a visualization. That's what an iterable Model class enables.

Check here for a Jupyter Notebook with an example:

Iterable Models

Note: the original version of the above graphic was dynamic, you can find it here.

Game of Life#

Live radCAD demo model on Streamlit

A simple game where at each timestep, the following transitions occur:

  1. Any live cell with fewer than two live neighbours dies, as if by underpopulation.
  2. Any live cell with two or three live neighbours lives on to the next generation.
  3. Any live cell with more than three live neighbours dies, as if by overpopulation.
  4. Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.

See examples/game_of_life/game-of-life.ipynb

Game of Life

Note: the original version of the above graphic was dynamic, you can find it here.

Predator-Prey#

A simple model that applies the two Lotka-Volterra differential equations, frequently used to describe the dynamics of biological systems in which two species interact:

Original models thanks to Danilo @danlessa!

For additional educational material about the Predator-Prey model, we recommend the cadCAD courses:

cadCAD Complete Foundations Bootcamp, which in Sections 5 and 6 introduces a model for an animal population interacting with the environment. The approach is carefully broken down into system requirements (including visual system mapping and mathematical specification), system design and system validation.

cadCAD Hacks - Season 1, which in Hack 2 provides a step-by-step introduction to the the Predator-Prey model with cadCAD.

Open-source Models Using radCAD#

Ethereum Economic Model by CADLabs#

A modular dynamical-systems model of Ethereum's validator economics.

This open-source model was developed in collaboration with the Ethereum Robust Incentives Group and funded by an Ethereum ESP (Ecosystem Support Program) grant. While originally scoped with purely modelling-educational intent as part of the cadCAD Edu online course cadCAD Masterclass: Ethereum Validator Economics, it has evolved to become a highly versatile, customizable and extensible research model that includes a list of model extension ideas. The model is focused on epoch- and population-level Ethereum validator economics across different deployment types and – at least in its initial setup – abstracts from slot- and agent-level dynamics.

To learn more about this model, here are the most useful links:

  • Model Assumptions: The model implements the official Ethereum Specification wherever possible, but rests on a few default network-level and validator-level assumptions detailed in the ASSUMPTIONS.md document.

  • Mathematical Model Specification: The Mathematical Model Specification articulates the relevant system dynamics as a state-space representation, the mathematical modelling paradigm underlying the cadCAD simulation library. It can be understood as a minimum viable formalism necessary to enable solid cadCAD modelling.

  • Differential Model Specification: The Differential Model Specification depicts the model's overall structure across System States, System Inputs, System Parameters, State Update Logic and System Metrics.

  • Educational online course cadCAD Masterclass: Ethereum Validator Economics

  • Github Repositorium

Fei Protocol Model by CADLabs#

A modular dynamical-systems model of Fei Protocol's Protocol-controlled Value (PCV) Monetary Policy and proposed FEI Savings Rate mechanism, based on the open-source Python library radCAD. The code repo is based on the CADLabs Ethereum Economic Model radCAD modelling & simulation project template.

Useful links:

Beacon Runner by Ethereum RIG#

Beacon Runner An agent-based model of Ethereum's Proof-of-Stake consensus layer

GEB Controller Simulations by Reflexer Protocol:#

GEB Controller Simulations

A Proportional-Integral-Derivative (PID) controller based upon a reference document approach for the Maker DAI market that was never implemented