Interactive supplement to the paper

"Geometrical frustration yields fiber formation in self-assembly"

by Martin Lenz and Thomas A. Witten

March, 2017

Each panel depicts one aggregate and contains a heading listing the asymmetry parameter \(k\) for irregular hexagons (or the polygon shape for other polygons), the rescaled surface tension \( \tilde{\sigma}\) and the growth procedure, as detailed in the text. Each column of panels differs only in \(\tilde{\sigma}\). The same list of \(\tilde{\sigma}\) values are used for all rows.

Orange colored polygons indicate seed regions present at the beginning of the growth process. Subsequently added polygons are shown in blue, with darkest blue for first added and lightest blue for last added. Orange lines indicate unjoined sides. The aggregates each have 150 added polygons. Images are scaled to the same size.

In cases where polygons overlap, the latest-added polygons appear in front, but orange lines for unjoined sides are shown for both exposed and hidden polygons. The 1st-7th row treat cases discussed in the main text, while the 8th-10th are discussed in the Supplementary text.

Click on "zoomable" above each aggregate to display a vectorial (indefinitely zoomable) image, allowing a detailed inspection of it. Click on the aggregate itself to show a movie of its assembly.

\(k = 2\) \(\tilde\sigma = 1.0\) (zoomable) |
\(k = 2\) \(\tilde\sigma = 1.1\) (zoomable) |
\(k = 2\) \(\tilde\sigma = 1.2\) (zoomable) |
\(k = 2\) \(\tilde\sigma = 1.3\) (zoomable) |
\(k = 2\) \(\tilde\sigma = 1.4\) (zoomable) |
\(k = 2\) \(\tilde\sigma = 1.5\) (zoomable) |
\(k = 2\) \(\tilde\sigma = 1.6\) (zoomable) |
\(k = 2\) \(\tilde\sigma = 1.7\) (zoomable) |
\(k = 2\) \(\tilde\sigma = 1.8\) (zoomable) |
\(k = 2\) \(\tilde\sigma = 1.9\) (zoomable) |
\(k = 2\) \(\tilde\sigma = 2.0\) (zoomable) |
\(k = 2\) \(\tilde\sigma = 2.1\) (zoomable) |
\(k = 2\) \(\tilde\sigma = 2.2\) (zoomable) |
\(k = 2\) \(\tilde\sigma = 2.3\) (zoomable) |
\(k = 2\) \(\tilde\sigma = 2.4\) (zoomable) |
\(k = 2\) \(\tilde\sigma = 2.5\) (zoomable) |
\(k = 2\) \(\tilde\sigma = 2.6\) (zoomable) |
\(k = 2\) \(\tilde\sigma = 2.7\) (zoomable) |
\(k = 2\) \(\tilde\sigma = 2.8\) (zoomable) |
\(k = 2\) \(\tilde\sigma = 2.9\) (zoomable) |

add & remove \(\tilde\sigma = 1.0\) (zoomable) |
add & remove \(\tilde\sigma = 1.1\) (zoomable) |
add & remove \(\tilde\sigma = 1.2\) (zoomable) |
add & remove \(\tilde\sigma = 1.3\) (zoomable) |
add & remove \(\tilde\sigma = 1.4\) (zoomable) |
add & remove \(\tilde\sigma = 1.5\) (zoomable) |
add & remove \(\tilde\sigma = 1.6\) (zoomable) |
add & remove \(\tilde\sigma = 1.7\) (zoomable) |
add & remove \(\tilde\sigma = 1.8\) (zoomable) |
add & remove \(\tilde\sigma = 1.9\) (zoomable) |
add & remove \(\tilde\sigma = 2.0\) (zoomable) |
add & remove \(\tilde\sigma = 2.1\) (zoomable) |
add & remove \(\tilde\sigma = 2.2\) (zoomable) |
add & remove \(\tilde\sigma = 2.3\) (zoomable) |
add & remove \(\tilde\sigma = 2.4\) (zoomable) |
add & remove \(\tilde\sigma = 2.5\) (zoomable) |
add & remove \(\tilde\sigma = 2.6\) (zoomable) |
add & remove \(\tilde\sigma = 2.7\) (zoomable) |
add & remove \(\tilde\sigma = 2.8\) (zoomable) |
add & remove \(\tilde\sigma = 2.9\) (zoomable) |

seeded \(\tilde\sigma = 1.0\) (zoomable) |
seeded \(\tilde\sigma = 1.1\) (zoomable) |
seeded \(\tilde\sigma = 1.2\) (zoomable) |
seeded \(\tilde\sigma = 1.3\) (zoomable) |
seeded \(\tilde\sigma = 1.4\) (zoomable) |
seeded \(\tilde\sigma = 1.5\) (zoomable) |
seeded \(\tilde\sigma = 1.6\) (zoomable) |
seeded \(\tilde\sigma = 1.7\) (zoomable) |
seeded \(\tilde\sigma = 1.8\) (zoomable) |
seeded \(\tilde\sigma = 1.9\) (zoomable) |
seeded \(\tilde\sigma = 2.0\) (zoomable) |
seeded \(\tilde\sigma = 2.1\) (zoomable) |
seeded \(\tilde\sigma = 2.2\) (zoomable) |
seeded \(\tilde\sigma = 2.3\) (zoomable) |
seeded \(\tilde\sigma = 2.4\) (zoomable) |
seeded \(\tilde\sigma = 2.5\) (zoomable) |
seeded \(\tilde\sigma = 2.6\) (zoomable) |
seeded \(\tilde\sigma = 2.7\) (zoomable) |
seeded \(\tilde\sigma = 2.8\) (zoomable) |
seeded \(\tilde\sigma = 2.9\) (zoomable) |

\(k = 1.01\) \(\tilde\sigma = 1.0\) (zoomable) |
\(k = 1.01\) \(\tilde\sigma = 1.1\) (zoomable) |
\(k = 1.01\) \(\tilde\sigma = 1.2\) (zoomable) |
\(k = 1.01\) \(\tilde\sigma = 1.3\) (zoomable) |
\(k = 1.01\) \(\tilde\sigma = 1.4\) (zoomable) |
\(k = 1.01\) \(\tilde\sigma = 1.5\) (zoomable) |
\(k = 1.01\) \(\tilde\sigma = 1.6\) (zoomable) |
\(k = 1.01\) \(\tilde\sigma = 1.7\) (zoomable) |
\(k = 1.01\) \(\tilde\sigma = 1.8\) (zoomable) |
\(k = 1.01\) \(\tilde\sigma = 1.9\) (zoomable) |
\(k = 1.01\) \(\tilde\sigma = 2.0\) (zoomable) |
\(k = 1.01\) \(\tilde\sigma = 2.1\) (zoomable) |
\(k = 1.01\) \(\tilde\sigma = 2.2\) (zoomable) |
\(k = 1.01\) \(\tilde\sigma = 2.3\) (zoomable) |
\(k = 1.01\) \(\tilde\sigma = 2.4\) (zoomable) |
\(k = 1.01\) \(\tilde\sigma = 2.5\) (zoomable) |
\(k = 1.01\) \(\tilde\sigma = 2.6\) (zoomable) |
\(k = 1.01\) \(\tilde\sigma = 2.7\) (zoomable) |
\(k = 1.01\) \(\tilde\sigma = 2.8\) (zoomable) |
\(k = 1.01\) \(\tilde\sigma = 2.9\) (zoomable) |

\(k = 4\) \(\tilde\sigma = 1.0\) (zoomable) |
\(k = 4\) \(\tilde\sigma = 1.1\) (zoomable) |
\(k = 4\) \(\tilde\sigma = 1.2\) (zoomable) |
\(k = 4\) \(\tilde\sigma = 1.3\) (zoomable) |
\(k = 4\) \(\tilde\sigma = 1.4\) (zoomable) |
\(k = 4\) \(\tilde\sigma = 1.5\) (zoomable) |
\(k = 4\) \(\tilde\sigma = 1.6\) (zoomable) |
\(k = 4\) \(\tilde\sigma = 1.7\) (zoomable) |
\(k = 4\) \(\tilde\sigma = 1.8\) (zoomable) |
\(k = 4\) \(\tilde\sigma = 1.9\) (zoomable) |
\(k = 4\) \(\tilde\sigma = 2.0\) (zoomable) |
\(k = 4\) \(\tilde\sigma = 2.1\) (zoomable) |
\(k = 4\) \(\tilde\sigma = 2.2\) (zoomable) |
\(k = 4\) \(\tilde\sigma = 2.3\) (zoomable) |
\(k = 4\) \(\tilde\sigma = 2.4\) (zoomable) |
\(k = 4\) \(\tilde\sigma = 2.5\) (zoomable) |
\(k = 4\) \(\tilde\sigma = 2.6\) (zoomable) |
\(k = 4\) \(\tilde\sigma = 2.7\) (zoomable) |
\(k = 4\) \(\tilde\sigma = 2.8\) (zoomable) |
\(k = 4\) \(\tilde\sigma = 2.9\) (zoomable) |

pentagons \(\tilde\sigma = 1.0\) (zoomable) |
pentagons \(\tilde\sigma = 1.1\) (zoomable) |
pentagons \(\tilde\sigma = 1.2\) (zoomable) |
pentagons \(\tilde\sigma = 1.3\) (zoomable) |
pentagons \(\tilde\sigma = 1.4\) (zoomable) |
pentagons \(\tilde\sigma = 1.5\) (zoomable) |
pentagons \(\tilde\sigma = 1.6\) (zoomable) |
pentagons \(\tilde\sigma = 1.7\) (zoomable) |
pentagons \(\tilde\sigma = 1.8\) (zoomable) |
pentagons \(\tilde\sigma = 1.9\) (zoomable) |
pentagons \(\tilde\sigma = 2.0\) (zoomable) |
pentagons \(\tilde\sigma = 2.1\) (zoomable) |
pentagons \(\tilde\sigma = 2.2\) (zoomable) |
pentagons \(\tilde\sigma = 2.3\) (zoomable) |
pentagons \(\tilde\sigma = 2.4\) (zoomable) |
pentagons \(\tilde\sigma = 2.5\) (zoomable) |
pentagons \(\tilde\sigma = 2.6\) (zoomable) |
pentagons \(\tilde\sigma = 2.7\) (zoomable) |
pentagons \(\tilde\sigma = 2.8\) (zoomable) |
pentagons \(\tilde\sigma = 2.9\) (zoomable) |

octagons \(\tilde\sigma = 1.0\) (zoomable) |
octagons \(\tilde\sigma = 1.1\) (zoomable) |
octagons \(\tilde\sigma = 1.2\) (zoomable) |
octagons \(\tilde\sigma = 1.3\) (zoomable) |
octagons \(\tilde\sigma = 1.4\) (zoomable) |
octagons \(\tilde\sigma = 1.5\) (zoomable) |
octagons \(\tilde\sigma = 1.6\) (zoomable) |
octagons \(\tilde\sigma = 1.7\) (zoomable) |
octagons \(\tilde\sigma = 1.8\) (zoomable) |
octagons \(\tilde\sigma = 1.9\) (zoomable) |
octagons \(\tilde\sigma = 2.0\) (zoomable) |
octagons \(\tilde\sigma = 2.1\) (zoomable) |
octagons \(\tilde\sigma = 2.2\) (zoomable) |
octagons \(\tilde\sigma = 2.3\) (zoomable) |
octagons \(\tilde\sigma = 2.4\) (zoomable) |
octagons \(\tilde\sigma = 2.5\) (zoomable) |
octagons \(\tilde\sigma = 2.6\) (zoomable) |
octagons \(\tilde\sigma = 2.7\) (zoomable) |
octagons \(\tilde\sigma = 2.8\) (zoomable) |
octagons \(\tilde\sigma = 2.9\) (zoomable) |

fiber seed \(\tilde\sigma = 1.0\) (zoomable) |
fiber seed \(\tilde\sigma = 1.1\) (zoomable) |
fiber seed \(\tilde\sigma = 1.2\) (zoomable) |
fiber seed \(\tilde\sigma = 1.3\) (zoomable) |
fiber seed \(\tilde\sigma = 1.4\) (zoomable) |
fiber seed \(\tilde\sigma = 1.5\) (zoomable) |
fiber seed \(\tilde\sigma = 1.6\) (zoomable) |
fiber seed \(\tilde\sigma = 1.7\) (zoomable) |
fiber seed \(\tilde\sigma = 1.8\) (zoomable) |
fiber seed \(\tilde\sigma = 1.9\) (zoomable) |
fiber seed \(\tilde\sigma = 2.0\) (zoomable) |
fiber seed \(\tilde\sigma = 2.1\) (zoomable) |
fiber seed \(\tilde\sigma = 2.2\) (zoomable) |
fiber seed \(\tilde\sigma = 2.3\) (zoomable) |
fiber seed \(\tilde\sigma = 2.4\) (zoomable) |
fiber seed \(\tilde\sigma = 2.5\) (zoomable) |
fiber seed \(\tilde\sigma = 2.6\) (zoomable) |
fiber seed \(\tilde\sigma = 2.7\) (zoomable) |
fiber seed \(\tilde\sigma = 2.8\) (zoomable) |
fiber seed \(\tilde\sigma = 2.9\) (zoomable) |

\(k = 6\) \(\tilde\sigma = 1.0\) (zoomable) |
\(k = 6\) \(\tilde\sigma = 1.1\) (zoomable) |
\(k = 6\) \(\tilde\sigma = 1.2\) (zoomable) |
\(k = 6\) \(\tilde\sigma = 1.3\) (zoomable) |
\(k = 6\) \(\tilde\sigma = 1.4\) (zoomable) |
\(k = 6\) \(\tilde\sigma = 1.5\) (zoomable) |
\(k = 6\) \(\tilde\sigma = 1.6\) (zoomable) |
\(k = 6\) \(\tilde\sigma = 1.7\) (zoomable) |
\(k = 6\) \(\tilde\sigma = 1.8\) (zoomable) |
\(k = 6\) \(\tilde\sigma = 1.9\) (zoomable) |
\(k = 6\) \(\tilde\sigma = 2.0\) (zoomable) |
\(k = 6\) \(\tilde\sigma = 2.1\) (zoomable) |
\(k = 6\) \(\tilde\sigma = 2.2\) (zoomable) |
\(k = 6\) \(\tilde\sigma = 2.3\) (zoomable) |
\(k = 6\) \(\tilde\sigma = 2.4\) (zoomable) |
\(k = 6\) \(\tilde\sigma = 2.5\) (zoomable) |
\(k = 6\) \(\tilde\sigma = 2.6\) (zoomable) |
\(k = 6\) \(\tilde\sigma = 2.7\) (zoomable) |
\(k = 6\) \(\tilde\sigma = 2.8\) (zoomable) |
\(k = 6\) \(\tilde\sigma = 2.9\) (zoomable) |

\(k = 10\) \(\tilde\sigma = 1.0\) (zoomable) |
\(k = 10\) \(\tilde\sigma = 1.1\) (zoomable) |
\(k = 10\) \(\tilde\sigma = 1.2\) (zoomable) |
\(k = 10\) \(\tilde\sigma = 1.3\) (zoomable) |
\(k = 10\) \(\tilde\sigma = 1.4\) (zoomable) |
\(k = 10\) \(\tilde\sigma = 1.5\) (zoomable) |
\(k = 10\) \(\tilde\sigma = 1.6\) (zoomable) |
\(k = 10\) \(\tilde\sigma = 1.7\) (zoomable) |
\(k = 10\) \(\tilde\sigma = 1.8\) (zoomable) |
\(k = 10\) \(\tilde\sigma = 1.9\) (zoomable) |
\(k = 10\) \(\tilde\sigma = 2.0\) (zoomable) |
\(k = 10\) \(\tilde\sigma = 2.1\) (zoomable) |
\(k = 10\) \(\tilde\sigma = 2.2\) (zoomable) |
\(k = 10\) \(\tilde\sigma = 2.3\) (zoomable) |
\(k = 10\) \(\tilde\sigma = 2.4\) (zoomable) |
\(k = 10\) \(\tilde\sigma = 2.5\) (zoomable) |
\(k = 10\) \(\tilde\sigma = 2.6\) (zoomable) |
\(k = 10\) \(\tilde\sigma = 2.7\) (zoomable) |
\(k = 10\) \(\tilde\sigma = 2.8\) (zoomable) |
\(k = 10\) \(\tilde\sigma = 2.9\) (zoomable) |