About

A powerful tool for studying complex dynamics. Inspired heavily by the following projects:

• Wolf Jung's Mandel (many of whose hotkeys are intentionally reused)
• Brian and Susanna Boyd's Dynamics Explorer
• Matt Noonan's FractalStream

Dynamo hopes to combine the strengths of these excellent tools.

Check out the web demo

The web demo linked above is the most convenient way to use Dynamo, but it is slower and is missing some features, most notably the ability to save images.

Features

• Over 100 built-in profiles for commonly studied dynamical systems
• Live Julia sets
• "Meta-parameter planes" (e.g. multiplier plane for Cubic Per(1, λ)) with live views of the child planes
• Live tracking for critical points and cycles
• Smooth coloring for both escaping and non-escaping components
• Period coloring
• Distance estimation
• External rays (working for quadratic polynomials and some other families, unstable in general)
• Equipotentials
• Optimized for performance

As of version 0.5.1, saved images now contain all annotations.

Installation

To install and run, just clone the repository, navigate to bin, and run cargo run -r.

You may need to first install Rust.

Alternatively, you can download a precompiled binary from the "Releases" tags on the right. Binaries are available for Linux, macOS, and Windows.

Usage

Navigation

• Z: zoom in to selection
• Ctrl-Z: zoom in far
• V: zoom out from selection
• Ctrl-V: zoom out far
• Shift-arrows: pan view
• Space: Center selection
• Shift-Space: Reset selection
• Home: Reset view and selection

Dynamics

• F: Apply map to selection [dynamical plane]
• Ctrl-F: Find/follow parameter of given preperiod/period near selection [active plane]
• E: External ray [active plane]
• Ctrl-X or Y: External ray to point [active plane]
• Ctrl-E: Draw all rays of a given period [active plane]
• Shift-O: Draw all rays in the orbit of a given angle [active plane]
• Shift-E: Extend ray outwards from selection (works in all families where gradient is implemented) [active plane]
• Shift-I: Extend ray inwards (can be numerically unstable) [active plane]
• Shift-T: Extend ray bidirectionally [active plane]
• G: Equipotential [active plane]
• M: Multiplier contour (only for marked cycle curves) [active plane]

Computation

• +: Increase max iters (x2)
• -: Decrease max iters (x1/2)
• Ctrl-S: save image (prompt in command line; currently does not include marked points/curves)
• L: Toggle Live Julia mode (update the child plane as the cursor moves in the parent plane)

Annotations

• I: Toggle selection [active plane]
• Ctrl-<N>: Toggle cycles of period <N>, if they are implemented for the given map [dynamical plane]
• Ctrl-Shift-<N>: Toggle component centers of period <N>, if they are implemented for the given family [parameter plane]
• P: Toggle critical points [dynamical plane]
• O: Draw orbit [parameter plane]
• C: Clear orbit [dynamical plane]
• Shift-C: Clear all marked curves [active plane]

Coloring

• R: Randomize palette
• W: White palette
• B: Black palette
• Ctrl-K: Save palette
• Ctrl-L: Load palette
• Up/Down: Change palette period
• Right/Left: Change palette phase
• 0: Internal coloration: Solid
• 1: Internal coloration: Period
• 2: Internal coloration: Period and Multiplier
• 3: Internal coloration: Multiplier
• 4: Internal coloration: Preperiod
• 5: Internal coloration: Potential of linearizing coordinate
• J: Toggle phase-based coloring for escape regions
• D: Toggle distance estimation

User Scripts (Experimental)

Users can now write scripts at runtime to study custom dynamical systems. Since this requires compiling code locally, Cargo is a strict dependency. Python3 and SymPy are also required for the transpilation process. The latter can be installed with pip install sympy.

To try out this feature, navigate to the project directory and run cargo run -rF scripting. This feature has been tested to work on Linux and Windows, but it remains highly experimental.

While not as flexible as manually editing profiles in Rust, scripts still allow for a lot of expressive power with minimal boilerplate.

Example syntax:

[metadata]
name = "QuadRat Per(2, μ)"
short_name = "quadrat_per_2_mu"

[names]
variable = "z"
selection = "t"

[constants]
mu = "2-i"

[parameters]
a = "t^2 * (mu + mu*t - 4) / 4"
b = "t * (mu*t - 4) / 4"

[dynamics]
start = 0
map = "(z^2 + a)/(z^2 + b)"

Planned Features

• Live Julia sets
• Mark orbits
• Marked points
• 🔨 External rays
• Equipotentials
• Saving improvements
  • Save/load palettes
  • Save images
    • Marked points/curves in saved images
  • Save program state
  • User-friendly save dialog
• Menu items for most/all actions
• Command-line integration
• Internal coloration
• Drag to pan/zoom
• Descend to child for multi-parameter systems
• Solve for critical points and $n$-cycles automatically
• 🔨 User-friendly scripting interface
• Switch to stable channel
• Implement web interface
  • Fix broken clicking in web UI
  • Fix slow initial rendering in web UI