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fractal

23 motifs. Import them from geomotif.motifs, or build one by name with registry.create("fractal.apollonian").

fractal.apollonian

fractal.apollonian

Circles packed into circles, filling every gap they leave.

from geomotif import save_svg
from geomotif.motifs import ApollonianGasket

motif = ApollonianGasket()
save_svg(motif.build(), "fractal.apollonian.svg", width=320, height=320)

geomotif render fractal.apollonian --out fractal.apollonian.svg

{
  "geomotif": "1.3.1",
  "motif": "fractal.apollonian",
  "params": {
    "depth": 5,
    "radius": 150.0,
    "min_radius": 0.004,
    "center": [
      0.0,
      0.0
    ]
  }
}
Parameters
Name Type Default
depth int 5
radius float 150.0
min_radius float 0.004
center Point (0.0, 0.0)

fractal.cantor

fractal.cantor

Take out the middle third. Repeat. Stack the rounds to see it happen.

from geomotif import save_svg
from geomotif.motifs import CantorSet

motif = CantorSet()
save_svg(motif.build(), "fractal.cantor.svg", width=320, height=320)

geomotif render fractal.cantor --out fractal.cantor.svg

{
  "geomotif": "1.3.1",
  "motif": "fractal.cantor",
  "params": {
    "depth": 6,
    "width": 240.0,
    "gap": 14.0,
    "center": [
      0.0,
      0.0
    ]
  }
}
Parameters
Name Type Default
depth int 6
width float 240.0
gap float 14.0
center Point (0.0, 0.0)

fractal.dragon

fractal.dragon

The Heighway dragon: fold a strip of paper in half, repeatedly, unfold.

from geomotif import save_svg
from geomotif.motifs import DragonCurve

motif = DragonCurve()
save_svg(motif.build(), "fractal.dragon.svg", width=320, height=320)

geomotif render fractal.dragon --out fractal.dragon.svg

{
  "geomotif": "1.3.1",
  "motif": "fractal.dragon",
  "params": {
    "depth": 10,
    "step": 1.0,
    "start_angle": 0.0
  }
}
Parameters
Name Type Default
depth int 10
step float 1.0
start_angle float 0.0

fractal.gosper

fractal.gosper

The flowsnake: a space-filling curve on a hexagonal grid.

from geomotif import save_svg
from geomotif.motifs import GosperCurve

motif = GosperCurve()
save_svg(motif.build(), "fractal.gosper.svg", width=320, height=320)

geomotif render fractal.gosper --out fractal.gosper.svg

{
  "geomotif": "1.3.1",
  "motif": "fractal.gosper",
  "params": {
    "depth": 4,
    "step": 1.0,
    "start_angle": 0.0
  }
}
Parameters
Name Type Default
depth int 4
step float 1.0
start_angle float 0.0

fractal.h-tree

fractal.h-tree

An H whose serifs are smaller H's, and so on down.

from geomotif import save_svg
from geomotif.motifs import HTree

motif = HTree()
save_svg(motif.build(), "fractal.h-tree.svg", width=320, height=320)

geomotif render fractal.h-tree --out fractal.h-tree.svg

{
  "geomotif": "1.3.1",
  "motif": "fractal.h-tree",
  "params": {
    "depth": 6,
    "size": 220.0,
    "center": [
      0.0,
      0.0
    ]
  }
}
Parameters
Name Type Default
depth int 6
size float 220.0
center Point (0.0, 0.0)

fractal.hilbert

fractal.hilbert

The space-filling curve that keeps neighbours together.

from geomotif import save_svg
from geomotif.motifs import HilbertCurve

motif = HilbertCurve()
save_svg(motif.build(), "fractal.hilbert.svg", width=320, height=320)

geomotif render fractal.hilbert --out fractal.hilbert.svg

{
  "geomotif": "1.3.1",
  "motif": "fractal.hilbert",
  "params": {
    "depth": 5,
    "step": 1.0,
    "start_angle": 0.0
  }
}
Parameters
Name Type Default
depth int 5
step float 1.0
start_angle float 0.0

fractal.koch

fractal.koch

The original: replace the middle third of every segment with a spike.

from geomotif import save_svg
from geomotif.motifs import KochCurve

motif = KochCurve()
save_svg(motif.build(), "fractal.koch.svg", width=320, height=320)

geomotif render fractal.koch --out fractal.koch.svg

{
  "geomotif": "1.3.1",
  "motif": "fractal.koch",
  "params": {
    "depth": 4,
    "step": 1.0,
    "start_angle": 0.0
  }
}
Parameters
Name Type Default
depth int 4
step float 1.0
start_angle float 0.0

fractal.koch-antisnowflake

fractal.koch-antisnowflake

The snowflake with its spikes turned inward, which is a different shape.

from geomotif import save_svg
from geomotif.motifs import KochAntisnowflake

motif = KochAntisnowflake()
save_svg(motif.build(), "fractal.koch-antisnowflake.svg", width=320, height=320)

geomotif render fractal.koch-antisnowflake --out fractal.koch-antisnowflake.svg

{
  "geomotif": "1.3.1",
  "motif": "fractal.koch-antisnowflake",
  "params": {
    "depth": 4,
    "step": 1.0,
    "start_angle": 0.0
  }
}
Parameters
Name Type Default
depth int 4
step float 1.0
start_angle float 0.0

fractal.koch-snowflake

fractal.koch-snowflake

Three Koch curves around a triangle: finite area, infinite perimeter.

from geomotif import save_svg
from geomotif.motifs import KochSnowflake

motif = KochSnowflake()
save_svg(motif.build(), "fractal.koch-snowflake.svg", width=320, height=320)

geomotif render fractal.koch-snowflake --out fractal.koch-snowflake.svg

{
  "geomotif": "1.3.1",
  "motif": "fractal.koch-snowflake",
  "params": {
    "depth": 4,
    "step": 1.0,
    "start_angle": 0.0
  }
}
Parameters
Name Type Default
depth int 4
step float 1.0
start_angle float 0.0

fractal.levy-c

fractal.levy-c

Paul Levy's C curve: two half-size copies at right angles, forever.

from geomotif import save_svg
from geomotif.motifs import LevyCCurve

motif = LevyCCurve()
save_svg(motif.build(), "fractal.levy-c.svg", width=320, height=320)

geomotif render fractal.levy-c --out fractal.levy-c.svg

{
  "geomotif": "1.3.1",
  "motif": "fractal.levy-c",
  "params": {
    "depth": 10,
    "step": 1.0,
    "start_angle": 0.0
  }
}
Parameters
Name Type Default
depth int 10
step float 1.0
start_angle float 0.0

fractal.minkowski

fractal.minkowski

Koch's idea on a square grid: a battlement instead of a spike.

from geomotif import save_svg
from geomotif.motifs import MinkowskiSausage

motif = MinkowskiSausage()
save_svg(motif.build(), "fractal.minkowski.svg", width=320, height=320)

geomotif render fractal.minkowski --out fractal.minkowski.svg

{
  "geomotif": "1.3.1",
  "motif": "fractal.minkowski",
  "params": {
    "depth": 3,
    "step": 1.0,
    "start_angle": 0.0
  }
}
Parameters
Name Type Default
depth int 3
step float 1.0
start_angle float 0.0

fractal.minkowski-island

fractal.minkowski-island

Four Minkowski sausages around a square: the quadratic Koch island.

from geomotif import save_svg
from geomotif.motifs import MinkowskiIsland

motif = MinkowskiIsland()
save_svg(motif.build(), "fractal.minkowski-island.svg", width=320, height=320)

geomotif render fractal.minkowski-island --out fractal.minkowski-island.svg

{
  "geomotif": "1.3.1",
  "motif": "fractal.minkowski-island",
  "params": {
    "depth": 3,
    "step": 1.0,
    "start_angle": 0.0
  }
}
Parameters
Name Type Default
depth int 3
step float 1.0
start_angle float 0.0

fractal.moore

fractal.moore

Hilbert's curve closed into a loop.

from geomotif import save_svg
from geomotif.motifs import MooreCurve

motif = MooreCurve()
save_svg(motif.build(), "fractal.moore.svg", width=320, height=320)

geomotif render fractal.moore --out fractal.moore.svg

{
  "geomotif": "1.3.1",
  "motif": "fractal.moore",
  "params": {
    "depth": 4,
    "step": 1.0,
    "start_angle": 0.0
  }
}
Parameters
Name Type Default
depth int 4
step float 1.0
start_angle float 0.0

fractal.peano

fractal.peano

The first space-filling curve ever published, from 1890.

from geomotif import save_svg
from geomotif.motifs import PeanoCurve

motif = PeanoCurve()
save_svg(motif.build(), "fractal.peano.svg", width=320, height=320)

geomotif render fractal.peano --out fractal.peano.svg

{
  "geomotif": "1.3.1",
  "motif": "fractal.peano",
  "params": {
    "depth": 3,
    "step": 1.0,
    "start_angle": 0.0
  }
}
Parameters
Name Type Default
depth int 3
step float 1.0
start_angle float 0.0

fractal.pythagoras-tree

fractal.pythagoras-tree

Squares on the legs of right triangles, all the way up.

from geomotif import save_svg
from geomotif.motifs import PythagorasTree

motif = PythagorasTree()
save_svg(motif.build(), "fractal.pythagoras-tree.svg", width=320, height=320)

geomotif render fractal.pythagoras-tree --out fractal.pythagoras-tree.svg

{
  "geomotif": "1.3.1",
  "motif": "fractal.pythagoras-tree",
  "params": {
    "depth": 8,
    "size": 60.0,
    "lean": 0.7853981633974483,
    "base": [
      0.0,
      0.0
    ]
  }
}
Parameters
Name Type Default
depth int 8
size float 60.0
lean float 0.7853981633974483
base Point (0.0, 0.0)

fractal.sierpinski-arrowhead

fractal.sierpinski-arrowhead

The gasket approached along a curve instead of through a triangle.

from geomotif import save_svg
from geomotif.motifs import SierpinskiArrowhead

motif = SierpinskiArrowhead()
save_svg(motif.build(), "fractal.sierpinski-arrowhead.svg", width=320, height=320)

geomotif render fractal.sierpinski-arrowhead --out fractal.sierpinski-arrowhead.svg

{
  "geomotif": "1.3.1",
  "motif": "fractal.sierpinski-arrowhead",
  "params": {
    "depth": 6,
    "step": 1.0,
    "start_angle": 0.0
  }
}
Parameters
Name Type Default
depth int 6
step float 1.0
start_angle float 0.0

fractal.sierpinski-carpet

fractal.sierpinski-carpet

A square with its middle ninth removed, then again in each ninth.

from geomotif import save_svg
from geomotif.motifs import SierpinskiCarpet

motif = SierpinskiCarpet()
save_svg(motif.build(), "fractal.sierpinski-carpet.svg", width=320, height=320)

geomotif render fractal.sierpinski-carpet --out fractal.sierpinski-carpet.svg

{
  "geomotif": "1.3.1",
  "motif": "fractal.sierpinski-carpet",
  "params": {
    "depth": 4,
    "size": 200.0,
    "center": [
      0.0,
      0.0
    ]
  }
}
Parameters
Name Type Default
depth int 4
size float 200.0
center Point (0.0, 0.0)

fractal.sierpinski-triangle

fractal.sierpinski-triangle

The gasket, drawn as one unbroken stroke that closes on itself.

from geomotif import save_svg
from geomotif.motifs import SierpinskiTriangle

motif = SierpinskiTriangle()
save_svg(motif.build(), "fractal.sierpinski-triangle.svg", width=320, height=320)

geomotif render fractal.sierpinski-triangle --out fractal.sierpinski-triangle.svg

{
  "geomotif": "1.3.1",
  "motif": "fractal.sierpinski-triangle",
  "params": {
    "depth": 5,
    "step": 1.0,
    "start_angle": 0.0
  }
}
Parameters
Name Type Default
depth int 5
step float 1.0
start_angle float 0.0

fractal.terdragon

fractal.terdragon

The dragon done in thirds: one segment becomes three at 120 degrees.

from geomotif import save_svg
from geomotif.motifs import Terdragon

motif = Terdragon()
save_svg(motif.build(), "fractal.terdragon.svg", width=320, height=320)

geomotif render fractal.terdragon --out fractal.terdragon.svg

{
  "geomotif": "1.3.1",
  "motif": "fractal.terdragon",
  "params": {
    "depth": 6,
    "step": 1.0,
    "start_angle": 0.0
  }
}
Parameters
Name Type Default
depth int 6
step float 1.0
start_angle float 0.0

fractal.twindragon

fractal.twindragon

Two Heighway dragons back to back, enclosing a region that tiles.

from geomotif import save_svg
from geomotif.motifs import TwinDragon

motif = TwinDragon()
save_svg(motif.build(), "fractal.twindragon.svg", width=320, height=320)

geomotif render fractal.twindragon --out fractal.twindragon.svg

{
  "geomotif": "1.3.1",
  "motif": "fractal.twindragon",
  "params": {
    "depth": 9,
    "step": 1.0,
    "start_angle": 0.0
  }
}
Parameters
Name Type Default
depth int 9
step float 1.0
start_angle float 0.0

fractal.vicsek

fractal.vicsek

The box fractal: a plus sign made of plus signs.

from geomotif import save_svg
from geomotif.motifs import VicsekFractal

motif = VicsekFractal()
save_svg(motif.build(), "fractal.vicsek.svg", width=320, height=320)

geomotif render fractal.vicsek --out fractal.vicsek.svg

{
  "geomotif": "1.3.1",
  "motif": "fractal.vicsek",
  "params": {
    "depth": 3,
    "step": 1.0,
    "start_angle": 0.0
  }
}
Parameters
Name Type Default
depth int 3
step float 1.0
start_angle float 0.0

points.barnsley-fern

points.barnsley-fern

Four affine maps and a coin, producing a fern.

from geomotif import save_svg
from geomotif.motifs import BarnsleyFern

motif = BarnsleyFern(count=4000)
save_svg(motif.build(), "points.barnsley-fern.svg", width=320, height=320)

geomotif render points.barnsley-fern --out points.barnsley-fern.svg

{
  "geomotif": "1.3.1",
  "motif": "points.barnsley-fern",
  "params": {
    "count": 4000,
    "size": 300.0,
    "seed": 0,
    "center": [
      0.0,
      0.0
    ]
  }
}
Parameters
Name Type Default
count int 40000
size float 300.0
seed int 0
center Point (0.0, 0.0)

points.ifs

points.ifs

The chaos game: pick a map at random, apply it, plot the point, repeat.

from geomotif import save_svg
from geomotif.motifs import IFSAttractor

motif = IFSAttractor(count=4000)
save_svg(motif.build(), "points.ifs.svg", width=320, height=320)

geomotif render points.ifs --out points.ifs.svg

{
  "geomotif": "1.3.1",
  "motif": "points.ifs",
  "params": {
    "maps": [
      {
        "$type": "geomotif.motifs.fractals.IFSMap",
        "transform": {
          "$type": "geomotif.core.transform.Affine",
          "a": 0.5,
          "b": 0.0,
          "c": 0.0,
          "d": 0.5,
          "e": 0.0,
          "f": 0.0
        },
        "weight": 1.0
      },
      {
        "$type": "geomotif.motifs.fractals.IFSMap",
        "transform": {
          "$type": "geomotif.core.transform.Affine",
          "a": 0.5,
          "b": 0.0,
          "c": 0.0,
          "d": 0.5,
          "e": 0.5,
          "f": 0.0
        },
        "weight": 1.0
      },
      {
        "$type": "geomotif.motifs.fractals.IFSMap",
        "transform": {
          "$type": "geomotif.core.transform.Affine",
          "a": 0.5,
          "b": 0.0,
          "c": 0.0,
          "d": 0.5,
          "e": 0.25,
          "f": 0.4330127018922193
        },
        "weight": 1.0
      }
    ],
    "count": 4000,
    "size": 240.0,
    "seed": 0,
    "center": [
      0.0,
      0.0
    ]
  }
}
Parameters
Name Type Default
maps tuple[IFSMap, ...] a tuple
count int 20000
size float 240.0
seed int 0
center Point (0.0, 0.0)