switzel / fractal

Various fractal scripts

Various fractal scripts

fractal contains scripts for a few different types of fractals, plus a bit of non-fractal mathematical exploration. The repo started as a tutorial for the Python programming language inside Otherlab. In addition to very simple examples (L-system curves, noise curves, and a poker-based fractal), it contains code to generated so-called "developing fractal curves" illustrating the refinement of L-system curves as a smooth surface:

Geoffrey Irving and Henry Segerman, "Developing fractal curves" (in review).

The license is standard three-clause BSD (see the included LICENSE file or LICENSE).

Dependencies

The simple pure Python fractals depend on

• python >= 2.6: A scripting language
• numpy >= 1.5: Efficient multidimensional arrays for Python
• scipy: Scientific computation for Python
• matplotlib: Python plotting

Mixed Python/C++ code such as developing fractal curves (dragon.py and render-dragon) additionally depend directly on

• geode: Otherlab computational geometry library
• other/gui: Otherlab gui library
• mitsuba >= 0.4.1: Physically based rendering

geode has a few more indirect dependencies (boost, scons).

Unfortunately, other/gui is not yet open source, so the interactive features of dragon.py and other 3D interactive scripts will not work outside of Otherlab. We will be releasing and open source version soon, at which point fractal will be updated accordingly. Note that dragon.py can be run in console mode without other/gui and then visualized and rendered via Mitsuba.

Setup

The simple scripts can be run immediately if their dependencies are available. For scripts which use C++ (anything that fails on import geode or import fractal_helper), first install geode via the instructions at https://github.com/otherlab/geode. Then build the C++ components of fractal via

git clone https://github.com/otherlab/fractal.git
cd fractal
ln -s <path-to-geode>/config.py # If geode required configuration
scons -j 5

If geode was built in place and not installed, add the following lines to config.py to tell fractal where to find it:

# In config.py
geode_dir = '<path-to-geode>'
geode_include = [geode_dir]
geode_libpath = [geode_dir+'/build/$arch/$type/lib']

Simple scripts

The simple scripts are run as follows:

cd other/fractal
./basics
./poker
./laplace
./noise
./l-system # List available kinds
./l-system koch # Visualize a Koch snowflake

Developing fractal curves

If other/gui is available, dragon.py can be run without arguments and all parameters adjusted interactively. Otherwise, it can run in console mode with --console 1 to dump out data for visualization in other programs. There are two modes: instanced (the default) and single mesh, controlled with --instanced <flag>. Single mesh mode generates a single smooth surface (suitable for 3D printing with an appropriate --thickness value). Instanced mode splits the surface into self-similar patches for efficient rendering in Mitsuba, with the benefit that each patch isomophism class can be given a different pretty color. See render-dragon for the commands used in the "Developing fractal curves" paper. Here is one example:

# Generate a level 13 dragon curve, writing mitsuba data to gen-dragon, and view it with Mitsuba
./dragon.py --type dragon --level 13 --smooth 4 --border-layers 4 --thickness 0.2 --ground 1 --rotation=0,-1,0,0 --mitsuba-dir gen-dragon --console 1
./render-dragon --gui 1 --view front --data gen-dragon

# Generate a level 11 dragon curve, writing a single mesh to dragon.stl
./dragon.py --type dragon --level 11 --smooth 3 --border-crease 0 --thickness 0.8 --thickness-alpha .8 --instance 0 -o dragon.stl --console 1

Hyperbolic tesselations

To see a triangular tiling of part of hyperbolic space represented in the Poincare disk model (https://en.wikipedia.org/wiki/Poincare_disk), run

./poincare --help # For available options
./poincare
./poincare --degree 8 --level 4

To (attempt to) discretely isometrically embed the tiling in 3D Euclidean space, run

./poincare --mode flop <options>

This will use other/gui if available and fall back to matplotlib otherwise (in which case it will be impossible to change options after startup). To save the mesh to a file on startup, use

./poincare --mode flop --autosave poincare.obj