README.md

This was a re-implementation of lamination-builder that runs in python without dependencies on a browser and focusing on animations and convenient generation of figures. Instead it uses Manim, and which has several dependencies. The scope of the project has expanded as my reaserch has pergressed, and it now contains allmost all the scripts used in my reaserch.

Installation:

Please refer to to manim's installation instructions. It and its dependencies are required, with the possible exception of tex. Afterward, you can simply run

pip install manim_lamination_builder

Example Uses:

generate the rabbit pullback tree through generation 5

from manim import config

# import ligth_theme # (download from https://gist.github.com/abul4fia/353b9a2c3d000088a82175fa64e0ce24#file-ligth_theme-py)
from manim_lamination_builder import PullBackTree, parse_lamination

start = parse_lamination("""{polygons:[['_100','_010','_001']],degree:2}""")
tree = PullBackTree.build(start, 5)

lams = list(filter(lambda lam: lam.trapped_criticality() == 0, tree.flatten()[-1]))
config.preview = True
tree.show_pullback_tree()

render multiple laminations in one image

python -m manim_lamination_builder file.json5

The input format is as follows: A json or json5 list of laminations to be placed in the figure (tilling is a best effort left to right and top to bottom placemen). The blank lamination is permitted.

[
  {
    polygons:[["_001","_010","_100"]],
    chords:[["_1","2"]],
    points: ["3"],
    degree: 4
  },
  {
    "polygons": [["0_003", "0_030", "0_300"], 
      ["1_003", "3_030", "3_300"], 
      ["2_003", "2_030", "2_300"], 
      ["3_003", "1_030", "1_300"]], 
    "chords": [], 
    "points": [], 
    "degree": 4
  },
  { degree: 4}
]

generate and render laminations to verify my research

from manim import tempconfig
from manim_lamination_builder import generate_unicritical_lamination, Main


with tempconfig({"quality": "high_quality", "preview": True}):
    Main(generate_unicritical_lamination(4, 3)).render()

Alternately, you might want to specify the rotational shape by hand:

from manim_lamination_builder import generate_sibling_portraits, parse_lamination, Main
from manim import tempconfig

shape = parse_lamination("""{polygons:[['_002','_020','_200']],degree:3}""").polygons[0]

portraits = generate_sibling_portraits(shape)

with tempconfig({"quality": "high_quality", "preview": True}):
    Main(portraits).render()

animate the leaves and points moving to their images

Please note that the animation does over its duration what sigma_3 does in one step. Moreover, this relies on the understanding that sigma_d is a dilation of angular position with wrapping (by a factor of d). So the forgotten digit is recorded and used to determine how many times to wrap around, which might not always be desirable.

from manim import Scene, WHITE, tempconfig
from manim_lamination_builder import (
    parse_lamination,
    curried_colorize_with_respect_to,
    sigma,
    AnimateLamination,
)


class MyScene(Scene):
    def construct(self):
        initial = parse_lamination(
            '{polygons: [["_200","_002","_020"]], points:[0.1,"200","201"], degree: 3 }'
        )

        initial.auto_populate()
        initial.colorizer = curried_colorize_with_respect_to(initial.polygons[0])
        final = initial.apply_function(sigma)
        mob = initial.build(3)
        mob.submobjects[2].set_color("#008080")
        self.add(mob)
        self.wait(2)
        self.play(AnimateLamination(initial, final, start_mobject=mob, run_time=5))
        self.wait(2)


with tempconfig(
    {"quality": "high_quality", "preview": True, "background_color": WHITE}
):
    scene = MyScene()
    scene.render()

Developments

Feature requests will be entertained, however this is intended to be used in combination with other tools like latex and your own python scripts. I hope this is a reasonable API.

License

Licensed under the The AGPLv3 License (AGPLv3) Copyright (c) 2023 Forrest M. Hilton [email protected] You should have received a copy of the GNU Affero General Public License along with this program. If not, see http://www.gnu.org/licenses/.