Aggregates resulting from our growth algorithm

Interactive supplement to the paper
"Geometrical frustration yields fiber formation in self-assembly"
by Martin Lenz and Thomas A. Witten
March, 2017

Legend

Each panel depicts one aggregate and contains a heading listing the rescaled surface tension \( \tilde{\sigma}\). By default its constitutive polygons are irregular hexagons with the asymmetry parameter \(k = 2\) grown by sequential addition seeded from a single polygon; any deviation from this situation is also stated in the heading. 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.

Instructions

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.

Data

\(k = 2\)
\(\tilde\sigma = 1.0\) (zoomable)
 1606_0000		 \(k = 2\)
\(\tilde\sigma = 1.1\) (zoomable)
 1606_0001		 \(k = 2\)
\(\tilde\sigma = 1.2\) (zoomable)
 1606_0002		 \(k = 2\)
\(\tilde\sigma = 1.3\) (zoomable)
 1606_0003		 \(k = 2\)
\(\tilde\sigma = 1.4\) (zoomable)
 1606_0004		 \(k = 2\)
\(\tilde\sigma = 1.5\) (zoomable)
 1606_0005		 \(k = 2\)
\(\tilde\sigma = 1.6\) (zoomable)
 1606_0006		 \(k = 2\)
\(\tilde\sigma = 1.7\) (zoomable)
 1606_0007		 \(k = 2\)
\(\tilde\sigma = 1.8\) (zoomable)
 1606_0008		 \(k = 2\)
\(\tilde\sigma = 1.9\) (zoomable)
 1606_0009		 \(k = 2\)
\(\tilde\sigma = 2.0\) (zoomable)
 1606_0010		 \(k = 2\)
\(\tilde\sigma = 2.1\) (zoomable)
 1606_0011		 \(k = 2\)
\(\tilde\sigma = 2.2\) (zoomable)
 1606_0012		 \(k = 2\)
\(\tilde\sigma = 2.3\) (zoomable)
 1606_0013		 \(k = 2\)
\(\tilde\sigma = 2.4\) (zoomable)
 1606_0014		 \(k = 2\)
\(\tilde\sigma = 2.5\) (zoomable)
 1606_0015		 \(k = 2\)
\(\tilde\sigma = 2.6\) (zoomable)
 1606_0016		 \(k = 2\)
\(\tilde\sigma = 2.7\) (zoomable)
 1606_0017		 \(k = 2\)
\(\tilde\sigma = 2.8\) (zoomable)
 1606_0018		 \(k = 2\)
\(\tilde\sigma = 2.9\) (zoomable)
 1606_0019
add & remove
\(\tilde\sigma = 1.0\) (zoomable)
 1606_0020		 add & remove
\(\tilde\sigma = 1.1\) (zoomable)
 1606_0021		 add & remove
\(\tilde\sigma = 1.2\) (zoomable)
 1606_0022		 add & remove
\(\tilde\sigma = 1.3\) (zoomable)
 1606_0023		 add & remove
\(\tilde\sigma = 1.4\) (zoomable)
 1606_0024		 add & remove
\(\tilde\sigma = 1.5\) (zoomable)
 1606_0025		 add & remove
\(\tilde\sigma = 1.6\) (zoomable)
 1606_0026		 add & remove
\(\tilde\sigma = 1.7\) (zoomable)
 1606_0027		 add & remove
\(\tilde\sigma = 1.8\) (zoomable)
 1606_0028		 add & remove
\(\tilde\sigma = 1.9\) (zoomable)
 1606_0029		 add & remove
\(\tilde\sigma = 2.0\) (zoomable)
 1606_0030		 add & remove
\(\tilde\sigma = 2.1\) (zoomable)
 1606_0031		 add & remove
\(\tilde\sigma = 2.2\) (zoomable)
 1606_0032		 add & remove
\(\tilde\sigma = 2.3\) (zoomable)
 1606_0033		 add & remove
\(\tilde\sigma = 2.4\) (zoomable)
 1606_0034		 add & remove
\(\tilde\sigma = 2.5\) (zoomable)
 1606_0035		 add & remove
\(\tilde\sigma = 2.6\) (zoomable)
 1606_0036		 add & remove
\(\tilde\sigma = 2.7\) (zoomable)
 1606_0037		 add & remove
\(\tilde\sigma = 2.8\) (zoomable)
 1606_0038		 add & remove
\(\tilde\sigma = 2.9\) (zoomable)
 1606_0039
bulk seed
\(\tilde\sigma = 1.0\) (zoomable)
 1606_0140		 bulk seed
\(\tilde\sigma = 1.1\) (zoomable)
 1606_0141		 bulk seed
\(\tilde\sigma = 1.2\) (zoomable)
 1606_0142		 bulk seed
\(\tilde\sigma = 1.3\) (zoomable)
 1606_0143		 bulk seed
\(\tilde\sigma = 1.4\) (zoomable)
 1606_0144		 bulk seed
\(\tilde\sigma = 1.5\) (zoomable)
 1606_0145		 bulk seed
\(\tilde\sigma = 1.6\) (zoomable)
 1606_0146		 bulk seed
\(\tilde\sigma = 1.7\) (zoomable)
 1606_0147		 bulk seed
\(\tilde\sigma = 1.8\) (zoomable)
 1606_0148		 bulk seed
\(\tilde\sigma = 1.9\) (zoomable)
 1606_0149		 bulk seed
\(\tilde\sigma = 2.0\) (zoomable)
 1606_0150		 bulk seed
\(\tilde\sigma = 2.1\) (zoomable)
 1606_0151		 bulk seed
\(\tilde\sigma = 2.2\) (zoomable)
 1606_0152		 bulk seed
\(\tilde\sigma = 2.3\) (zoomable)
 1606_0153		 bulk seed
\(\tilde\sigma = 2.4\) (zoomable)
 1606_0154		 bulk seed
\(\tilde\sigma = 2.5\) (zoomable)
 1606_0155		 bulk seed
\(\tilde\sigma = 2.6\) (zoomable)
 1606_0156		 bulk seed
\(\tilde\sigma = 2.7\) (zoomable)
 1606_0157		 bulk seed
\(\tilde\sigma = 2.8\) (zoomable)
 1606_0158		 bulk seed
\(\tilde\sigma = 2.9\) (zoomable)
 1606_0159
\(k = 1.01\)
\(\tilde\sigma = 1.0\) (zoomable)
 1606_0160		 \(k = 1.01\)
\(\tilde\sigma = 1.1\) (zoomable)
 1606_0161		 \(k = 1.01\)
\(\tilde\sigma = 1.2\) (zoomable)
 1606_0162		 \(k = 1.01\)
\(\tilde\sigma = 1.3\) (zoomable)
 1606_0163		 \(k = 1.01\)
\(\tilde\sigma = 1.4\) (zoomable)
 1606_0164		 \(k = 1.01\)
\(\tilde\sigma = 1.5\) (zoomable)
 1606_0165		 \(k = 1.01\)
\(\tilde\sigma = 1.6\) (zoomable)
 1606_0166		 \(k = 1.01\)
\(\tilde\sigma = 1.7\) (zoomable)
 1606_0167		 \(k = 1.01\)
\(\tilde\sigma = 1.8\) (zoomable)
 1606_0168		 \(k = 1.01\)
\(\tilde\sigma = 1.9\) (zoomable)
 1606_0169		 \(k = 1.01\)
\(\tilde\sigma = 2.0\) (zoomable)
 1606_0170		 \(k = 1.01\)
\(\tilde\sigma = 2.1\) (zoomable)
 1606_0171		 \(k = 1.01\)
\(\tilde\sigma = 2.2\) (zoomable)
 1606_0172		 \(k = 1.01\)
\(\tilde\sigma = 2.3\) (zoomable)
 1606_0173		 \(k = 1.01\)
\(\tilde\sigma = 2.4\) (zoomable)
 1606_0174		 \(k = 1.01\)
\(\tilde\sigma = 2.5\) (zoomable)
 1606_0175		 \(k = 1.01\)
\(\tilde\sigma = 2.6\) (zoomable)
 1606_0176		 \(k = 1.01\)
\(\tilde\sigma = 2.7\) (zoomable)
 1606_0177		 \(k = 1.01\)
\(\tilde\sigma = 2.8\) (zoomable)
 1606_0178		 \(k = 1.01\)
\(\tilde\sigma = 2.9\) (zoomable)
 1606_0179
\(k = 4\)
\(\tilde\sigma = 1.0\) (zoomable)
 1606_0080		 \(k = 4\)
\(\tilde\sigma = 1.1\) (zoomable)
 1606_0081		 \(k = 4\)
\(\tilde\sigma = 1.2\) (zoomable)
 1606_0082		 \(k = 4\)
\(\tilde\sigma = 1.3\) (zoomable)
 1606_0083		 \(k = 4\)
\(\tilde\sigma = 1.4\) (zoomable)
 1606_0084		 \(k = 4\)
\(\tilde\sigma = 1.5\) (zoomable)
 1606_0085		 \(k = 4\)
\(\tilde\sigma = 1.6\) (zoomable)
 1606_0086		 \(k = 4\)
\(\tilde\sigma = 1.7\) (zoomable)
 1606_0087		 \(k = 4\)
\(\tilde\sigma = 1.8\) (zoomable)
 1606_0088		 \(k = 4\)
\(\tilde\sigma = 1.9\) (zoomable)
 1606_0089		 \(k = 4\)
\(\tilde\sigma = 2.0\) (zoomable)
 1606_0090		 \(k = 4\)
\(\tilde\sigma = 2.1\) (zoomable)
 1606_0091		 \(k = 4\)
\(\tilde\sigma = 2.2\) (zoomable)
 1606_0092		 \(k = 4\)
\(\tilde\sigma = 2.3\) (zoomable)
 1606_0093		 \(k = 4\)
\(\tilde\sigma = 2.4\) (zoomable)
 1606_0094		 \(k = 4\)
\(\tilde\sigma = 2.5\) (zoomable)
 1606_0095		 \(k = 4\)
\(\tilde\sigma = 2.6\) (zoomable)
 1606_0096		 \(k = 4\)
\(\tilde\sigma = 2.7\) (zoomable)
 1606_0097		 \(k = 4\)
\(\tilde\sigma = 2.8\) (zoomable)
 1606_0098		 \(k = 4\)
\(\tilde\sigma = 2.9\) (zoomable)
 1606_0099
pentagons
\(\tilde\sigma = 1.0\) (zoomable)
 1606_0100		 pentagons
\(\tilde\sigma = 1.1\) (zoomable)
 1606_0101		 pentagons
\(\tilde\sigma = 1.2\) (zoomable)
 1606_0102		 pentagons
\(\tilde\sigma = 1.3\) (zoomable)
 1606_0103		 pentagons
\(\tilde\sigma = 1.4\) (zoomable)
 1606_0104		 pentagons
\(\tilde\sigma = 1.5\) (zoomable)
 1606_0105		 pentagons
\(\tilde\sigma = 1.6\) (zoomable)
 1606_0106		 pentagons
\(\tilde\sigma = 1.7\) (zoomable)
 1606_0107		 pentagons
\(\tilde\sigma = 1.8\) (zoomable)
 1606_0108		 pentagons
\(\tilde\sigma = 1.9\) (zoomable)
 1606_0109		 pentagons
\(\tilde\sigma = 2.0\) (zoomable)
 1606_0110		 pentagons
\(\tilde\sigma = 2.1\) (zoomable)
 1606_0111		 pentagons
\(\tilde\sigma = 2.2\) (zoomable)
 1606_0112		 pentagons
\(\tilde\sigma = 2.3\) (zoomable)
 1606_0113		 pentagons
\(\tilde\sigma = 2.4\) (zoomable)
 1606_0114		 pentagons
\(\tilde\sigma = 2.5\) (zoomable)
 1606_0115		 pentagons
\(\tilde\sigma = 2.6\) (zoomable)
 1606_0116		 pentagons
\(\tilde\sigma = 2.7\) (zoomable)
 1606_0117		 pentagons
\(\tilde\sigma = 2.8\) (zoomable)
 1606_0118		 pentagons
\(\tilde\sigma = 2.9\) (zoomable)
 1606_0119
octagons
\(\tilde\sigma = 1.0\) (zoomable)
 1606_0120		 octagons
\(\tilde\sigma = 1.1\) (zoomable)
 1606_0121		 octagons
\(\tilde\sigma = 1.2\) (zoomable)
 1606_0122		 octagons
\(\tilde\sigma = 1.3\) (zoomable)
 1606_0123		 octagons
\(\tilde\sigma = 1.4\) (zoomable)
 1606_0124		 octagons
\(\tilde\sigma = 1.5\) (zoomable)
 1606_0125		 octagons
\(\tilde\sigma = 1.6\) (zoomable)
 1606_0126		 octagons
\(\tilde\sigma = 1.7\) (zoomable)
 1606_0127		 octagons
\(\tilde\sigma = 1.8\) (zoomable)
 1606_0128		 octagons
\(\tilde\sigma = 1.9\) (zoomable)
 1606_0129		 octagons
\(\tilde\sigma = 2.0\) (zoomable)
 1606_0130		 octagons
\(\tilde\sigma = 2.1\) (zoomable)
 1606_0131		 octagons
\(\tilde\sigma = 2.2\) (zoomable)
 1606_0132		 octagons
\(\tilde\sigma = 2.3\) (zoomable)
 1606_0133		 octagons
\(\tilde\sigma = 2.4\) (zoomable)
 1606_0134		 octagons
\(\tilde\sigma = 2.5\) (zoomable)
 1606_0135		 octagons
\(\tilde\sigma = 2.6\) (zoomable)
 1606_0136		 octagons
\(\tilde\sigma = 2.7\) (zoomable)
 1606_0137		 octagons
\(\tilde\sigma = 2.8\) (zoomable)
 1606_0138		 octagons
\(\tilde\sigma = 2.9\) (zoomable)
 1606_0139
fiber seed
\(\tilde\sigma = 1.0\) (zoomable)
 1606_0200		 fiber seed
\(\tilde\sigma = 1.1\) (zoomable)
 1606_0201		 fiber seed
\(\tilde\sigma = 1.2\) (zoomable)
 1606_0202		 fiber seed
\(\tilde\sigma = 1.3\) (zoomable)
 1606_0203		 fiber seed
\(\tilde\sigma = 1.4\) (zoomable)
 1606_0204		 fiber seed
\(\tilde\sigma = 1.5\) (zoomable)
 1606_0205		 fiber seed
\(\tilde\sigma = 1.6\) (zoomable)
 1606_0206		 fiber seed
\(\tilde\sigma = 1.7\) (zoomable)
 1606_0207		 fiber seed
\(\tilde\sigma = 1.8\) (zoomable)
 1606_0208		 fiber seed
\(\tilde\sigma = 1.9\) (zoomable)
 1606_0209		 fiber seed
\(\tilde\sigma = 2.0\) (zoomable)
 1606_0210		 fiber seed
\(\tilde\sigma = 2.1\) (zoomable)
 1606_0211		 fiber seed
\(\tilde\sigma = 2.2\) (zoomable)
 1606_0212		 fiber seed
\(\tilde\sigma = 2.3\) (zoomable)
 1606_0213		 fiber seed
\(\tilde\sigma = 2.4\) (zoomable)
 1606_0214		 fiber seed
\(\tilde\sigma = 2.5\) (zoomable)
 1606_0215		 fiber seed
\(\tilde\sigma = 2.6\) (zoomable)
 1606_0216		 fiber seed
\(\tilde\sigma = 2.7\) (zoomable)
 1606_0217		 fiber seed
\(\tilde\sigma = 2.8\) (zoomable)
 1606_0218		 fiber seed
\(\tilde\sigma = 2.9\) (zoomable)
 1606_0219
\(k = 6\)
\(\tilde\sigma = 1.0\) (zoomable)
 1606_0240		 \(k = 6\)
\(\tilde\sigma = 1.1\) (zoomable)
 1606_0241		 \(k = 6\)
\(\tilde\sigma = 1.2\) (zoomable)
 1606_0242		 \(k = 6\)
\(\tilde\sigma = 1.3\) (zoomable)
 1606_0243		 \(k = 6\)
\(\tilde\sigma = 1.4\) (zoomable)
 1606_0244		 \(k = 6\)
\(\tilde\sigma = 1.5\) (zoomable)
 1606_0245		 \(k = 6\)
\(\tilde\sigma = 1.6\) (zoomable)
 1606_0246		 \(k = 6\)
\(\tilde\sigma = 1.7\) (zoomable)
 1606_0247		 \(k = 6\)
\(\tilde\sigma = 1.8\) (zoomable)
 1606_0248		 \(k = 6\)
\(\tilde\sigma = 1.9\) (zoomable)
 1606_0249		 \(k = 6\)
\(\tilde\sigma = 2.0\) (zoomable)
 1606_0250		 \(k = 6\)
\(\tilde\sigma = 2.1\) (zoomable)
 1606_0251		 \(k = 6\)
\(\tilde\sigma = 2.2\) (zoomable)
 1606_0252		 \(k = 6\)
\(\tilde\sigma = 2.3\) (zoomable)
 1606_0253		 \(k = 6\)
\(\tilde\sigma = 2.4\) (zoomable)
 1606_0254		 \(k = 6\)
\(\tilde\sigma = 2.5\) (zoomable)
 1606_0255		 \(k = 6\)
\(\tilde\sigma = 2.6\) (zoomable)
 1606_0256		 \(k = 6\)
\(\tilde\sigma = 2.7\) (zoomable)
 1606_0257		 \(k = 6\)
\(\tilde\sigma = 2.8\) (zoomable)
 1606_0258		 \(k = 6\)
\(\tilde\sigma = 2.9\) (zoomable)
 1606_0259
\(k = 10\)
\(\tilde\sigma = 1.0\) (zoomable)
 1606_0260		 \(k = 10\)
\(\tilde\sigma = 1.1\) (zoomable)
 1606_0261		 \(k = 10\)
\(\tilde\sigma = 1.2\) (zoomable)
 1606_0262		 \(k = 10\)
\(\tilde\sigma = 1.3\) (zoomable)
 1606_0263		 \(k = 10\)
\(\tilde\sigma = 1.4\) (zoomable)
 1606_0264		 \(k = 10\)
\(\tilde\sigma = 1.5\) (zoomable)
 1606_0265		 \(k = 10\)
\(\tilde\sigma = 1.6\) (zoomable)
 1606_0266		 \(k = 10\)
\(\tilde\sigma = 1.7\) (zoomable)
 1606_0267		 \(k = 10\)
\(\tilde\sigma = 1.8\) (zoomable)
 1606_0268		 \(k = 10\)
\(\tilde\sigma = 1.9\) (zoomable)
 1606_0269		 \(k = 10\)
\(\tilde\sigma = 2.0\) (zoomable)
 1606_0270		 \(k = 10\)
\(\tilde\sigma = 2.1\) (zoomable)
 1606_0271		 \(k = 10\)
\(\tilde\sigma = 2.2\) (zoomable)
 1606_0272		 \(k = 10\)
\(\tilde\sigma = 2.3\) (zoomable)
 1606_0273		 \(k = 10\)
\(\tilde\sigma = 2.4\) (zoomable)
 1606_0274		 \(k = 10\)
\(\tilde\sigma = 2.5\) (zoomable)
 1606_0275		 \(k = 10\)
\(\tilde\sigma = 2.6\) (zoomable)
 1606_0276		 \(k = 10\)
\(\tilde\sigma = 2.7\) (zoomable)
 1606_0277		 \(k = 10\)
\(\tilde\sigma = 2.8\) (zoomable)
 1606_0278		 \(k = 10\)
\(\tilde\sigma = 2.9\) (zoomable)
 1606_0279