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‎.github/workflows/docs.yml

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name: Docs
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name: Build docs with Simulate for Web
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on:
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workflow_dispatch:
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jobs:
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with:
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python-version: '3.7'
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architecture: 'x64'
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- uses: subosito/flutter-action@v1
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with:
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channel: 'stable'
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- run: flutter pub get
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- run: flutter build web --release --base-href /simulate/web/
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- name: Install dependencies
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run: |
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python3 -m pip install --upgrade pip
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run: mkdocs build
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- name: Add latest web build and deploy
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run: |
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git clone -b web https://github.com/cod-ed/simulate web
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mv web/web/ site/
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mv build/web/ site/
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mkdocs gh-deploy --dirty

‎.gitmodules

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[submodule "site"]
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path = site
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url = https://github.com/cod-ed/simulate.git
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url = https://github.com/builtree/simulate.git
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branch = gh-pages

‎README.md

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<p align="center">
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<a href="https://github.com/cod-ed/simulate">
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<img src="https://raw.githubusercontent.com/cod-ed/assets/simulate/documentation/SimulateTitle.svg" width=40%>
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<a href="https://github.com/builtree/simulate">
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<img src="https://raw.githubusercontent.com/builtree/assets/simulate/documentation/SimulateTitle.svg" width=40%>
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</img>
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</a>
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</p>
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Welcome to Simulate! Simulate aims to be a collection of simulations and visualizations from various domains like mathematics, physics, computer science etc. in a cross platform app made using [Flutter](https://flutter.dev/).
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You can find out more about Simulate and how it works or how you can share ideas and contribute to the project [here](https://cod-ed.github.io/simulate/).
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You can find out more about Simulate and how it works or how you can share ideas and contribute to the project [here](https://builtree.github.io/simulate/).
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<p align="center">
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<a href="https://cod-ed.github.io/simulate/web">
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<img src="https://raw.githubusercontent.com/cod-ed/assets/simulate/documentation/LaunchWebApp.svg" width=200px>
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<a href="https://builtree.github.io/simulate/web">
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<img src="https://raw.githubusercontent.com/builtree/assets/simulate/documentation/LaunchWebApp.svg" width=200px>
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</img>
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</a>
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</p>
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3. Don't hesitate in asking questions, we'll be happy to help
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All further guidelines can be found [here](https://cod-ed.github.io/simulate/contributing).
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All further guidelines can be found [here](https://builtree.github.io/simulate/contributing).

‎docs/contributing.md

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#### Adding a new Simulation:
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1. Got an idea? Discuss the idea on [gitter](https://gitter.im/codEd-org/simulate#) or just open an issue with this [template](https://github.com/cod-ed/simulate/issues/new?assignees=&labels=enhancement%2C+new+simulation%2C+simulations&template=simulation-request.md&title=simulation%3A+%5BSIMULATION+TITLE%5D). If the maintainers find it interesting, the issue will be labeled accepted. If you want to work on it and don't know how to implement it yet, we'll help you get it done.
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2. Even if you don't have an idea but are interested in working on one, checkout the [accepted simulation ideas](https://github.com/cod-ed/simulate/issues?q=is%3Aopen+is%3Aissue+label%3Aaccepted+label%3A%22new+simulation%22) and get assigned.
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1. Got an idea? Discuss the idea on [gitter](https://gitter.im/codEd-org/simulate#) or just open an issue with this [template](https://github.com/builtree/simulate/issues/new?assignees=&labels=enhancement%2C+new+simulation%2C+simulations&template=simulation-request.md&title=simulation%3A+%5BSIMULATION+TITLE%5D). If the maintainers find it interesting, the issue will be labeled accepted. If you want to work on it and don't know how to implement it yet, we'll help you get it done.
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2. Even if you don't have an idea but are interested in working on one, checkout the [accepted simulation ideas](https://github.com/builtree/simulate/issues?q=is%3Aopen+is%3Aissue+label%3Aaccepted+label%3A%22new+simulation%22) and get assigned.
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3. You can start working now! Make sure you ask for help when needed, it's okay to get stuck.
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‎docs/index.md

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Welcome to Simulate! Simulate aims to be a collection of simulations and visualizations from various domains like mathematics, physics, computer science etc. in a cross platform app made using [Flutter](https://flutter.dev/). The outcomes of these simulations mostly are really smooth (thanks to Flutter) and extremely beautiful (thanks to mathematics/sciences behind it).
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<center>
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[![Simulate for Web](https://raw.githubusercontent.com/cod-ed/assets/simulate/documentation/LaunchWebApp.svg){: style="width:300px"}](https://cod-ed.github.io/simulate/web){: target="_blank"}
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[![Simulate for Web](https://raw.githubusercontent.com/builtree/assets/simulate/documentation/LaunchWebApp.svg){: style="width:300px"}](https://builtree.github.io/simulate/web){: target="_blank"}
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</center>
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‎docs/simulations/algorithms/ToothpickPattern.md

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# Toothpick Pattern
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---
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![ToothpickPatternLight](https://raw.githubusercontent.com/cod-ed/simulate/master/assets/simulations/ToothpickPatternLight.png){: style="height:200px", align=right}
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![ToothpickPatternLight](https://raw.githubusercontent.com/builtree/simulate/master/assets/simulations/ToothpickPatternLight.png){: style="height:200px", align=right}
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<p align="justify">
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The toothpick sequence in geometry is a 2D pattern sequence which is based on the previous
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[^1]: https://en.wikipedia.org/wiki/Ulam%E2%80%93Warburton_automaton
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=== "Light Mode"
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![ToothpickPatternLight](https://raw.githubusercontent.com/cod-ed/assets/simulate/simulations/ToothpickPatternLight.png){: style="width:300px"}
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![ToothpickPatternLight](https://raw.githubusercontent.com/builtree/assets/simulate/simulations/ToothpickPatternLight.png){: style="width:300px"}
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=== "Dark Mode"
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![ToothpickPatternDark](https://raw.githubusercontent.com/cod-ed/assets/simulate/simulations/ToothpickPatternDark.png){: style="width:300px"}
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![ToothpickPatternDark](https://raw.githubusercontent.com/builtree/assets/simulate/simulations/ToothpickPatternDark.png){: style="width:300px"}
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!!! tip "Fun Fact"
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The toothpick is considered such an essential that even Swiss Army knives - a popular brand of multi-function tools - have included one in their product

‎docs/simulations/index.md

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| Simulation | Category | Description | Image |
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| :---------------: | :---------------: | :---------------: | :---------------: |
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| Bubble Sort (Bars) | Algorithms | Bubble sort is a sorting algorithm that repeatedly steps through the list by comparing adjacent elements and swaps them if they are in the wrong order | ![Bubble Sort](https://raw.githubusercontent.com/cod-ed/simulate/master/assets/simulations/BubbleSortLight.png) |
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| Epicycloid Pattern(Pencil of Lines) | Mathematics | a.k.a hypercycloid, is a plane curve created by tracing a chosen point on the edge of a circle of radius r rolling on the outside of a circle of radius R | ![Epicycloid Pattern](https://raw.githubusercontent.com/cod-ed/assets/simulate/icons/Epicycloid1Light.png) |
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| Epicycloid Curve | Mathematics | a.k.a hypercycloid, is a plane curve created by tracing a chosen point on the edge of a circle of radius r rolling on the outside of a circle of radius R | ![Epicycloid Curve](https://raw.githubusercontent.com/cod-ed/assets/simulate/icons/EpicycloidLight.png) |
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| [Fourier Series](mathematics/FourierSeries.md) | Mathematics | A Fourier series is an expansion of a periodic function in terms of an infinite sum of sines and cosines | ![Fourier Series](https://raw.githubusercontent.com/cod-ed/assets/simulate/icons/FourierSeriesLight.png) |
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| Insertion Sort (Bars) | Algorithms | Insertion sort is a sorting algorithm that builds the final list one item at a time | ![Insertion Sort](https://raw.githubusercontent.com/cod-ed/simulate/master/assets/simulations/InsertionSortLight.png) |
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| [Lissajous Pattern](mathematics/LissajousPattern.md)| Mathematics | Lissajous pattern is generated by the junction of a pair of sinusoidal waves with axes that are perpendicular to one another |![Lissajous Pattern](https://raw.githubusercontent.com/cod-ed/assets/simulate/icons/LissajousCurveLight.png) |
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| [Maurer Rose Pattern](mathematics/MaurerRosePattern.md) | Mathematics | A Maurer Rose is a polygonal curve with vertices on a rose and can be described as a closed route in the polar plane | ![MaurerRose Pattern](https://raw.githubusercontent.com/cod-ed/assets/simulate/icons/MaurerRoseLight.png) |
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| Rose Pattern | Mathematics | A Rose pattern is generated by the junction of sinusoids plotted in polar coordinates | ![Rose Pattern](https://raw.githubusercontent.com/cod-ed/assets/simulate/icons/RosePatternLight.png) |
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| [Toothpick Pattern](algorithms/ToothpickPattern.md) | Algorithms | A Toothpick pattern is a sequence of 2D patterns formed by repeatedly adding line segments or _toothpicks_ to the previous pattern in the sequence. It starts with a single line segment | ![Toothpick Pattern](https://raw.githubusercontent.com/cod-ed/simulate/master/assets/simulations/ToothpickPatternLight.png) |
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| Bubble Sort (Bars) | Algorithms | Bubble sort is a sorting algorithm that repeatedly steps through the list by comparing adjacent elements and swaps them if they are in the wrong order | ![Bubble Sort](https://raw.githubusercontent.com/builtree/simulate/master/assets/simulations/BubbleSortLight.png) |
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| Epicycloid Pattern(Pencil of Lines) | Mathematics | a.k.a hypercycloid, is a plane curve created by tracing a chosen point on the edge of a circle of radius r rolling on the outside of a circle of radius R | ![Epicycloid Pattern](https://raw.githubusercontent.com/builtree/assets/simulate/icons/Epicycloid1Light.png) |
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| Epicycloid Curve | Mathematics | a.k.a hypercycloid, is a plane curve created by tracing a chosen point on the edge of a circle of radius r rolling on the outside of a circle of radius R | ![Epicycloid Curve](https://raw.githubusercontent.com/builtree/assets/simulate/icons/EpicycloidLight.png) |
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| [Fourier Series](mathematics/FourierSeries.md) | Mathematics | A Fourier series is an expansion of a periodic function in terms of an infinite sum of sines and cosines | ![Fourier Series](https://raw.githubusercontent.com/builtree/assets/simulate/icons/FourierSeriesLight.png) |
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| Insertion Sort (Bars) | Algorithms | Insertion sort is a sorting algorithm that builds the final list one item at a time | ![Insertion Sort](https://raw.githubusercontent.com/builtree/simulate/master/assets/simulations/InsertionSortLight.png) |
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| [Lissajous Pattern](mathematics/LissajousPattern.md)| Mathematics | Lissajous pattern is generated by the junction of a pair of sinusoidal waves with axes that are perpendicular to one another |![Lissajous Pattern](https://raw.githubusercontent.com/builtree/assets/simulate/icons/LissajousCurveLight.png) |
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| [Maurer Rose Pattern](mathematics/MaurerRosePattern.md) | Mathematics | A Maurer Rose is a polygonal curve with vertices on a rose and can be described as a closed route in the polar plane | ![MaurerRose Pattern](https://raw.githubusercontent.com/builtree/assets/simulate/icons/MaurerRoseLight.png) |
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| Rose Pattern | Mathematics | A Rose pattern is generated by the junction of sinusoids plotted in polar coordinates | ![Rose Pattern](https://raw.githubusercontent.com/builtree/assets/simulate/icons/RosePatternLight.png) |
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| [Toothpick Pattern](algorithms/ToothpickPattern.md) | Algorithms | A Toothpick pattern is a sequence of 2D patterns formed by repeatedly adding line segments or _toothpicks_ to the previous pattern in the sequence. It starts with a single line segment | ![Toothpick Pattern](https://raw.githubusercontent.com/builtree/simulate/master/assets/simulations/ToothpickPatternLight.png) |

‎docs/simulations/mathematics/FourierSeries.md

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# Fourier Series
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![FourierSeries](https://raw.githubusercontent.com/cod-ed/simulate/master/assets/simulations/FourierSeriesLight.png){: style="height:200px", align=right}
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![FourierSeries](https://raw.githubusercontent.com/builtree/simulate/master/assets/simulations/FourierSeriesLight.png){: style="height:200px", align=right}
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A Fourier transform is a way of breaking down a complex function into (infinite) sums of sine and cosine waves. In short, given a smoothie, it finds its recipe. Fourier series is the Fourier transform of a periodic function and it aims to represent the periodic function as a sum of sinusoidal waves. It is analogous to the Taylor series, which represents functions as an infinite sum of monomial terms.</p>
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[^2]: https://upload.wikimedia.org/wikipedia/commons/1/1e/Fourier_series_sawtooth_wave_circles_animation.svg
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=== "Light Mode"
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![FourierSeriesLight](https://raw.githubusercontent.com/cod-ed/assets/simulate/simulations/FourierSeriesLight.png){: style="width:600px"}
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![FourierSeriesLight](https://raw.githubusercontent.com/builtree/assets/simulate/simulations/FourierSeriesLight.png){: style="width:600px"}
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![FourierSeriesDark](https://raw.githubusercontent.com/cod-ed/assets/simulate/simulations/FourierSeriesDark.png){: style="width:600px"}
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![FourierSeriesDark](https://raw.githubusercontent.com/builtree/assets/simulate/simulations/FourierSeriesDark.png){: style="width:600px"}
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‎docs/simulations/mathematics/LissajousPattern.md

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# Lissajous Pattern
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![LissajousPatternLight](https://raw.githubusercontent.com/cod-ed/simulate/master/assets/simulations/LissajousCurveLight.png){: style="height:200px", align=right}
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![LissajousPatternLight](https://raw.githubusercontent.com/builtree/simulate/master/assets/simulations/LissajousCurveLight.png){: style="height:200px", align=right}
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A Lissajous curve in mathematics, also known as Lissajous Figure or Bowditch curve is the
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![LissajousPatternLight](https://raw.githubusercontent.com/cod-ed/assets/simulate/simulations/LissajousCurveLight.png){: style="width:300px"}
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![LissajousPatternLight](https://raw.githubusercontent.com/builtree/assets/simulate/simulations/LissajousCurveLight.png){: style="width:300px"}
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![LissajousPatternDark](https://raw.githubusercontent.com/cod-ed/assets/simulate/simulations/LissajousCurveDark.png){: style="width:300px"}
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![LissajousPatternDark](https://raw.githubusercontent.com/builtree/assets/simulate/simulations/LissajousCurveDark.png){: style="width:300px"}
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The title sequence by John Whitney for Alfred Hitchcock's 1958 film Vertigo is based on Lissajous figures.

‎docs/simulations/mathematics/MaurerRosePattern.md

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# Maurer Rose Pattern
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![MaurerRoseLight](https://raw.githubusercontent.com/cod-ed/simulate/master/assets/simulations/MaurerRoseLight.png){: style="height:200px", align=right}
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![MaurerRoseLight](https://raw.githubusercontent.com/builtree/simulate/master/assets/simulations/MaurerRoseLight.png){: style="height:200px", align=right}
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![MaurerRoseLight](https://raw.githubusercontent.com/cod-ed/assets/simulate/simulations/MaurerRoseLight.png){: style="width:300px"}
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![MaurerRoseLight](https://raw.githubusercontent.com/builtree/assets/simulate/simulations/MaurerRoseLight.png){: style="width:300px"}
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![MaurerRoseDark](https://raw.githubusercontent.com/cod-ed/assets/simulate/simulations/MaurerRoseDark.png){: style="width:300px"}
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![MaurerRoseDark](https://raw.githubusercontent.com/builtree/assets/simulate/simulations/MaurerRoseDark.png){: style="width:300px"}

‎ios/Flutter/flutter_export_environment.sh

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‎lib/generated_plugin_registrant.dart

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‎lib/main.dart

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import 'package:flutter/material.dart';
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import 'package:provider/provider.dart';
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import 'package:simulate/src/data/simulations.dart';

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