Geometry placements

The geometry placements here were built using the FractalDNA package package in Python. Accompanying each geometry is the Python code to generate it.

These geometries are based on iterating a fractal L-string.

Square geometry

A square geometry can be easily generated using the X fractal seed.

Download with 1 iteration (link)
Download with 2 iteration (link)
Download with 3 iteration (link)
Download with 4 iterations (link)
Download with 5 iterations (link)
Download with 6 iterations (link)
Download with 7 iterations (link)
Download with 8 iterations (link)

# Start with the initial L-String X for a Hilbert Curve
initial_string = 'X'
# Iterate it as required (here, nn=3)
# for nn = 8, this takes about two hours on my MacBook Pro 16GB RAM
nn = 3
iterated_lstring = h.iterate_lstring(initial_string)
for _ in range(nn-1):
    iterated_lstring = h.iterate_lstring(iterated_lstring)

vf = v.VoxelisedFractal.fromLString(iterated_lstring, pbar=True)
vf.center_fractal()
# fig = vf.to_plot()
# fig.savefig('results/fractal-X-3-centred.svg')

# If you are saving a BIG fractal, try using the to_text() method instead
# as large dataframes are very slow to generate beyond 6 iterations.
# with open(f'results/fractal-X-{nn}-centred.csv', 'w') as ff:
#     ff.write(vf.to_text())
vf.to_frame().to_csv(f'results/fractal-X-{nn}-centred.csv', index=False, sep=' ')

Rectangular geometry

A square geometry can be easily generated using the XFXFX fractal seed.

The aspect ratio will be:

1x1x2 for XFX
1x1x3 for XFXFX
1x1x4 for XFXFXFX
and so on as the seed changes.
Download XFXFX iterated 2 times (link)
Download XFXFX iterated 3 times (link)
Download XFXFX iterated 4 times (link)

# Start with the initial L-String XFXFX for a Hilbert Curve
initial_string = 'XFXFX'
# Iterate it as required (here, nn=4)
nn = 4
iterated_lstring = h.iterate_lstring(initial_string)
for _ in range(nn-1):
    iterated_lstring = h.iterate_lstring(iterated_lstring)

vf = v.VoxelisedFractal.fromLString(iterated_lstring, pbar=True)
vf.center_fractal()
# fig = vf.to_plot()
# fig.savefig(f'results/fractal-XFXFX-{nn}-centred.svg')

vf.to_frame().to_csv(f'results/fractal-XFXFX-{nn}-centred.csv', index=False, sep=' ')

Generating geometries from a path

The voxelisation model can convert the path of this curve to a voxelised representation, of straight and curved boxes.

In this example we perform this on a text file with X/Y/Z columns (link) to produce this output file

df = pd.read_csv('example-path.csv', sep='\t')
fig = plt.figure()
ax = fig.add_subplot(111, projection="3d")
ax.plot(df.X, df.Y, df.Z)
fig.savefig('example-path.svg')

vf = v.VoxelisedFractal.from_path(df.values)
fig_fractal = vf.to_plot()
fig_fractal.savefig('example-path-voxels.svg')

vf.to_frame().to_csv('results/example-path-voxels.csv', sep=' ')

The below images show that the paths made by the voxelised geometry (right) are identical to those in the source geometry (left)

Generating random placements

It can be useful to generate randomised volumes for testing a simulation (see parameter study). This was the subject of this article.

To generate a randomised volume, the fractaldna.structure_models.random_placements is available.

In that paper, 200,000 non overlapping prisms were simulated in a r=3000nm ball. The prisms had dimensions 30x30x100nm and a sample file can be downloaded here.

Note that the saved file doesn’t contain the dimensions of the prisms as this is instead fed to the macro file directly.

from fractaldna.structure_models import random_placements as rp

# Generating 200,000 prisms can take around 4-5 hours and will slow down
# as more are added
prisms = rp.generate_non_overlapping_prisms(
    n_prisms=200_000,
    size=[30, 30, 100],  # nanometres
    rad=3000,  # nanometres
    early_exit=-1,
    verbose=True)

df = prisms.to_frame()
df.to_csv('results/prisms_200k_r3000.csv', sep=' ', index=False)