Creating 3D fractals in Blender using Lindenmayer Systems.
- Creating Lindenmayer System Fractals
- Creating Fractal Landscapes
- Running the 2D Heat Flow Simulation
- Gray Scott Parameters
- Building the Paper
Note that large fractals take quite some time to compose, and may even crash Blender, or in extreme circumstances your entire operating system.
Use the batch.sh script like so:
./batch.sh data/b3d.json --jobs 4This will use 4 Blender processes to create the data/b3d.blend Blender scene.
Doing so creates several new files in data/:
$ ls data/b3d*
data/b3d.blend data/b3d-cylinders.json data/b3d-job-0.blend data/b3d-job-1.blend data/b3d-job-2.blend data/b3d-job-3.blend data/b3d.jsonThe b3d-job-*-.blend files are the results of each individual job, and the data/b3d.blend is the
final Blender file containing the joined results.
Note that the results will contain however many objects as there were jobs -- that is, the joining process
does not join all the meshes, it just combines all the objects into one scene.
Then run
blender data/b3d.blendto view the wonderful results.
Use clean.sh to remove the intermediate generated files to save several gigabytes of disk space between runs.
The batch.sh script combines the scripts/generate.py, scripts/render.py, and scripts/join.py scripts, each with their own usage.
For simplicity's sake, we recommend using the wrapper batch.sh script which runs each of the listed scripts in the correct order, even if the number of jobs is set to 1.
Use scripts/landscapes.py to generate the fractal landscapes.
Its usage statement is given below
$ PYTHONPATH=$(pwd) python3 scripts/landscapes.py --help
usage: landscapes.py [-h] [--one] [--recursions RECURSIONS [RECURSIONS ...]]
[--scale SCALE [SCALE ...]] [--hurst HURST [HURST ...]]
[--seed SEED] [--sealevel SEALEVEL] [--title TITLE]
[--gui] [--output OUTPUT]
Generate fractal landscapes with the random midpoint displacement algorithm.
optional arguments:
-h, --help show this help message and exit
--one Generate a 1D heightmap.
--recursions RECURSIONS [RECURSIONS ...], -r RECURSIONS [RECURSIONS ...]
The number of recursive subdivisions.
--scale SCALE [SCALE ...], -s SCALE [SCALE ...]
The vertical scale.
--hurst HURST [HURST ...], -H HURST [HURST ...]
The Hurst roughness exponent.
--seed SEED The random seed.
--sealevel SEALEVEL, -l SEALEVEL
The landscape sealevel.
--title TITLE, -t TITLE
The plot title.
--gui Open the plot in a GUI window.
--output OUTPUT, -o OUTPUT
The file to save the plot to.
If multiple values for recursions, scale, or hurst are given, every
combination of the given parameters will be plotted on the same axis. It is
advisable to avoid plotting multiple 3D surface plots on the same axis.Notice the use of the PYTHONPATH environment variable to make the natural Python library discoverable to the landscapes.py script.
An example usage is given below to generate a 2D landscape
$ PYTHONPATH=$(pwd) python3 scripts/landscapes.py --gui -r5 -l -0.3 -H 0.7
seed: 2729300867Notice that if a seed is not given, a seed will be generated and the random number generator will be seeded so that each landscape is reproducible.
Use the scripts/heat.py script to run the 2D heatflow simulation.
Its usage statement is given below
$ PYTHONPATH=$(pwd) python3 scripts/heat.py --help
usage: heat.py [-h] [--ymin YMIN] [--ymax YMAX] [--rows ROWS] [--cols COLS]
[--timestep TIMESTEP] [--prows PROWS] [--pcols PCOLS]
[--title TITLE] [--output OUTPUT] [--gui]
Generate 2D heat diffusion plots with CAs.
optional arguments:
-h, --help show this help message and exit
--ymin YMIN The lower domain y boundary.
--ymax YMAX The upper domain y boundary.
--rows ROWS The number of cells to use along the y axis.
--cols COLS The number of cells to use along the x axis.
--timestep TIMESTEP, -i TIMESTEP
The time interval to generate subplots at.
--prows PROWS The number of rows of subplots.
--pcols PCOLS The number of columns of subplots
--title TITLE The plot title.
--output OUTPUT The output filename.
--gui Open the plot in a GUI window.Notice that there are options to generate subplots of several timeslices of the diffusion process. An example usage is given below.
$ PYTHONPATH=$(pwd) python3 scripts/heat.py --gui --timestep 1000 --rows 100 --cols 100The usage statement for the scripts/reaction.py is given below.
$ PYTHONPATH=$(pwd) python3 scripts/reaction.py --help
usage: reaction.py [-h] [--gui] [--output OUTPUT] [--title TITLE] [--uv]
[--size SIZE] [--ru RU] [--rv RV] [--feed FEED]
[--kill KILL] [--iterations ITERATIONS] [--radius RADIUS]
[--u0 U0] [--v0 V0] [--scale SCALE]
Run the Gray-Scott Model with configurable parameters.
optional arguments:
-h, --help show this help message and exit
--gui Open a GUI window displaying the plot.
--output OUTPUT, -o OUTPUT
The filename to save the results as.
--title TITLE The plot title.
--uv Plot both U and V concentrations.
--size SIZE, -n SIZE The grid size.
--ru RU The U diffusion rate.
--rv RV The V diffusion rate.
--feed FEED, -f FEED The U feed rate.
--kill KILL, -k KILL The U,V kill rate.
--iterations ITERATIONS, -i ITERATIONS
The number of iterations.
--radius RADIUS, -r RADIUS
The initial high concentration center radius.
--u0 U0 The initial high concentration center U concentration.
--v0 V0 The initial high concentration center V concentration.
--scale SCALE, -s SCALE
The scale of the initial uniform distribution.Notice that there are many tweakable parameters.
An example usage of the scripts/reaction.py script is shown below.
$ PYTHONPATH=$(pwd) python3 scripts/reaction.py \
--iterations 5000 \
--kill 0.05 \
--feed 0.017 \
--radius 5 \
--size 128 \
--title "Pattern $\\alpha$" \
--gui \
--output alpha.epsAll of the original patterns in Pearson's original work can be generated by the paper's makefile:
$ cd papers
$ make figuresThe paper can be built by running the included makefile.
However, note that doing so requires the appropriate Python libraries installed.
There is an included requirements.txt file containing the necessary libraries.
$ virtualenv ~/.virtualenvs/natural
$ source ~/.virtualenvs/natural/bin/activate
$ pip install -r requirements.txt
$ cd paper
$ make -j 8Also notice that most of the figures in the paper are generated as prerequisite steps in the build process, so the first time you build the paper will take quite some time. Be sure to enable parallel builds.