Strange Attractors Visualizer

A web application for visualizing strange attractors using TresJS and WASM.

Attractors

• Lorenz Attractor ($\sigma = 10, \rho = 28, \beta = \frac{8}{3}$)

$$ \begin{aligned} \dot{x} &= \sigma(y - x) \\ \dot{y} &= x(\rho - z) - y \\ \dot{z} &= xy - \beta z \\ \end{aligned} $$

• Rössler Attractor ($\alpha = 0.1, \beta = 0.1, \gamma = 14$)

$$ \begin{aligned} \dot{x} &= -y - z \\ \dot{y} &= x + \alpha y \\ \dot{z} &= \beta + z(x - \gamma) \\ \end{aligned} $$

• Thomas Attractor ($\beta = 0.208186$)

$$ \begin{aligned} \dot{x} &= \sin(y) - \beta x \\ \dot{y} &= \sin(z) - \beta y \\ \dot{z} &= \sin(x) - \beta z \\ \end{aligned} $$

• Dequan Li Attractor ($\alpha = 40, \beta = 1.833, \gamma = 0.16, \delta = 0.65, \varepsilon = 55, \zeta = 20$)

$$ \begin{aligned} \dot{x} &= \alpha (y - x) + \gamma x z \\ \dot{y} &= \varepsilon x + \zeta y - x z \\ \dot{z} &= \beta z + x y - \delta x^2 \\ \end{aligned} $$

• Newton-Leipnik Attractor ($\alpha = 0.4, \beta = 0.175$)

$$ \begin{aligned} \dot{x} &= y - \alpha x + 10 y z \\ \dot{y} &= -x - \alpha y + 5 x z \\ \dot{z} &= \beta z - 5 x y \\ \end{aligned} $$

• Nosé-Hoover Attractor ($\alpha = 1.5$)

$$ \begin{aligned} \dot{x} &= y \\ \dot{y} &= -x + y z \\ \dot{z} &= \alpha - y^2 \\ \end{aligned} $$

• Halvorsen Attractor ($\alpha = 1.4$)

$$ \begin{aligned} \dot{x} &= -\alpha x - 4 y - 4 z - y^2 \\ \dot{y} &= -\alpha y - 4 z - 4 x - z^2 \\ \dot{z} &= -\alpha z - 4 x - 4 y - x^2 \\ \end{aligned} $$

• Chen-Lee Attractor ($\alpha = 5, \beta = -10, \gamma = -0.38$)

$$ \begin{aligned} \dot{x} &= \alpha x - y z \\ \dot{y} &= \beta y + x z \\ \dot{z} &= \gamma z + \frac{1}{3} x y \\ \end{aligned} $$

• Bouali Attractor ($\alpha = 0.1, \beta = -0.1, \mu=1$)

$$ \begin{aligned} \dot{x} &= \alpha z - x (1 - y) \\ \dot{y} &= y (1 - x^2) \\ \dot{z} &= \beta x - \mu z (1 - y) \\ \end{aligned} $$

• Finance Attractor ($\alpha = 0.001, \beta = 0.2, \gamma = 1.1$)

$$ \begin{aligned} \dot{x} &= \left(\frac{1}{\beta} - \alpha\right) x + z + x y \\ \dot{y} &= -\beta y - x^2 \\ \dot{z} &= -\gamma z - x \\ \end{aligned} $$

• Arneodo Attractor ($\alpha = -5.5, \beta = 3.5, \gamma = -1$)

$$ \begin{aligned} \dot{x} &= y \\ \dot{y} &= z \\ \dot{z} &= - \alpha x - \beta y - z + \gamma x^3 \\ \end{aligned} $$

• Sprott B Attractor ($\alpha = 0.4, \beta = 1.2, \gamma = 1$)

$$ \begin{aligned} \dot{x} &= \alpha y z \\ \dot{y} &= x - \beta y \\ \dot{z} &= \gamma - x y \\ \end{aligned} $$

• Sprott-Linz F Attractor ($\alpha = 0.5$)

$$ \begin{aligned} \dot{x} &= y + z \\ \dot{y} &= - x + \alpha y \\ \dot{z} &= x^2 - z \\ \end{aligned} $$

• Dadras Attractor ($\alpha = 3, \beta = 2.7, \gamma = 1.7, \delta = 2, \varepsilon = 9$)

$$ \begin{aligned} \dot{x} &= y - \alpha x + \beta y z \\ \dot{y} &= \gamma y - x z + z \\ \dot{z} &= \delta x y - \varepsilon z \\ \end{aligned} $$

Approximation Solver

• Runge-Kutta 4th Order Method

$$ \begin{aligned} \dot{y} &= f(y) \\ k_1 &= f(y_n) \\ k_2 &= f(y_n + \frac{h}{2}k_1) \\ k_3 &= f(y_n + \frac{h}{2}k_2) \\ k_4 &= f(y_n + hk_3) \\ y_{n+1} &= y_n + \frac{h}{6}(k_1 + 2k_2 + 2k_3 + k_4) \\ \end{aligned} $$

Performance

• Refactor code to using Rust WebAssembly
  • FPS boost up to 2x

Setup

Make sure to install the dependencies:

# bun
bun install

You may also need Rust toolchain installed, and wasm-pack for building the Rust WebAssembly:

# rustup
rustup install stable
cargo install wasm-pack

Development Server

Start the development server on http://localhost:3000:

# bun
bun run wasm && bun run dev

Production

Build

Build the application for production:

# bun
bun run wasm && bun run build

Static Generation

Generate a static version of the application:

# bun
bun run wasm && bun run generate

Either way, it will generate a dist directory containing the static files that can be deployed to any static hosting service.

Locally Preview

Locally preview production build (by either build or generate):

# bun
bun run preview