snowflakes

A Python implementation of the snow crystal growth model of Gravner and Griffeath (2008), accelerated with Numba where it is installed and running on plain NumPy elsewhere, with a web app that grows crystals in the browser.

The web app

https://roytsmart.github.io/snowflakes/ grows a crystal on your phone or computer, starting from parameter sets from the paper's figures. It runs the model compiled from Rust to WebAssembly, a 30 KB module which computes exactly what this package computes in single precision, bit for bit; the tests check that the two agree.

To run it locally, build the kernel and serve the app:

cargo build --release --target wasm32-unknown-unknown --manifest-path rust/Cargo.toml
python web/serve.py

and open http://localhost:8000.

Installation

pip install git+https://github.com/roytsmart/snowflakes

Usage

Grow a stellar dendrite, with the parameters of Fig. 11 of the paper, from a single cell of ice:

import numpy as np
import snowflakes

a_0 = np.zeros((301, 301), dtype=bool)
a_0[150, 150] = True

a, b, c, d = snowflakes.snowflake(
    a_0=a_0,
    alpha=0.4,
    beta=1.6,
    gamma=0.0005,
    theta=0.025,
    kappa=0.005,
    mu=0.015,
    rho=0.635,
    num_steps=2000,
    num_frames=50,
)

a says which cells are attached to the crystal and b, c, and d hold the boundary mass, crystal mass, and vapor of each cell, in each of the 50 frames from the seed to the last step. sigma adds the paper's noise, with seed to make it repeatable, and dtype=np.float32 computes in single precision, which is faster.

snowflakes.initial() and snowflakes.step() advance a crystal a given number of updates at a time instead.

The grid is a triangular lattice stored on a square array, as in the paper: each cell neighbors the cells above, below, left, and right of it and the two along the diagonal from lower left to upper right, and the edges wrap around. To see the crystal with its true hexagonal symmetry, put the cell in row i and column j at (j + i / 2, i * sqrt(3) / 2).

Implementations

Steps i to iv of the model are implemented three times, which all compute the same thing bit for bit: the same operations, on the same values, in the same order.

• snowflakes/_numpy.py is the reference, vectorized with NumPy. It is used wherever Numba is missing.
• snowflakes/_numba.py makes three passes over the grid in parallel, and is used wherever Numba is installed. It is about six times faster than NumPy on one thread and over 7,000 updates per second on a 301 by 301 grid with many.
• rust/ is the kernel of the web app, with a C interface which JavaScript calls in WebAssembly. Built natively with cargo build --release, the tests call it with ctypes and compare it with the reference.

The tests also check that the deterministic model conserves mass and that its crystals keep their six-fold symmetry.