Conformal Mapper

WARNING: This is a purely vibe-coded repo. It is subsloptimal. I make no guarantees about anything; use at your own peril. The standard caveats apply. If symptoms persist, etc.

What

Applies conformal (angle-preserving) mappings to images, creating a new image with those transformations applied, and (optinally) an animation of the process. (Also, technically the last two transformations are not actually conformal, but they're here now so).

Available Mappings

Starting with this input image

a sampling of transformations goes as:

Mapping	Description	-s 0.5	-s 1.5	-s 2.5
mobius	Mobius transform
spiral	Logarithmic spiral
joukowski	Joukowski airfoil transform
exp	Complex exponential
log	Complex logarithm
power	Power mapping (z^n)
sin	Complex sine
inversion	Circle inversion (1/z)
swirl	Swirl distortion
droste	Droste effect (recursive zoom)

Installation

Using uv (recommended)

uv venv
source .venv/bin/activate  # On Windows: .venv\Scripts\activate
uv pip install -r requirements.txt

Using pip

python -m venv .venv
source .venv/bin/activate
pip install -r requirements.txt

Usage

Basic transformation

python conformal_map.py input.jpg -o output.png -m mobius

List available mappings

python conformal_map.py --list

Create animated GIF

python conformal_map.py input.jpg -g animation.gif -m swirl -n 60 --duration 30

Create MP4 video

python conformal_map.py input.jpg --mp4 animation.mp4 -m droste -n 60

Note: MP4 output requires ffmpeg to be installed.

Options

Option	Description
-o, --output	Output image path (default: output.png)
-m, --mapping	Conformal mapping to apply
-s, --scale	Scale factor for complex plane (default: 2.0)
-g, --gif	Output GIF path for animation
--mp4	Output MP4 path for animation
-n, --frames	Number of frames for animation (default: 30)
--duration	Duration per frame in ms (default: 50)
-l, --list	List available mappings

Running with uv (without installing)

uv run --with numpy --with pillow --with tqdm conformal_map.py input.jpg -m spiral -s 1.5