Filtered Specimens
  • Tile Shape
  • Tile-Tile Interaction
    Edge to edge
  • Granularity
  • Pattern & Layout
  • Tile Material
  • Joint Material
  • Function
    Structural support
    Surface interaction
Selected Organisms
Cartilaginous fish
Bony fish
Filtered samples
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Tile Shape
Tile shape plays a large role in how a tessellation is patterned. We define “shape” as the tile outline when looking down on the tiled surface (i.e. the tile’s apparent geometry projected on the XY plane). The 3D anatomy of many natural tessellations is yet to be described; we focus only on shapes and structures visible externally (e.g. in available images), ignoring overlaps, protrusions, or complex interlocks in the z-direction.
Tile-Tile Interaction
The mechanical behaviour of tilings is determined in part by how tiles physically interact with each other. This is determined by the shape of tiles and whether and how contact is maintained between them, either through direct contact or indirect contact via intervening joint materials (e.g. collagen connecting tiles).
In natural tessellations, the absolute size of a single tile can vary considerably, from micrometers to centimeters. Tessellations can also cover either entire organisms or just a portion of them; for example, some fish (e.g. sticklebacks, piranha) have only a single strip of tiles running down the body, while others are fully armored (e.g. gar, bichir). Regardless of absolute tile size, tile size *relative to the whole tiled area* (not necessarily the whole organism) can be a decisive factor in the architecture of the tiled surface. We classify relative scale of tiles as with sandpapers: as coarse, medium or fine grain. The number of tiles that define each grain type are estimated from available images, but should be considered approximate.
Pattern & Layout
At a more macroscopic size scale, beyond the size and number of tiles, the regularity and layout of a tessellation pattern dictates how it covers a surface. Even within a single organism, the tessellation pattern can vary in different regions. For example, in chiton (armored molluscs) the dorsal shell plates form a unidirectional and regular pattern, while the miniscule scales of the encircling girdle form a bi-directional (but also regular) pattern.
Tile Material & Joint Material
Biological materials are mostly composites involving multiple components. We define a tessellation’s materials by its dominant building blocks: the minerals, proteins, sugars, and other materials comprising the 'tiles' and the 'joints' connecting them. Notice how many tile materials involve both organic and inorganic constituents (e.g. protein and mineral in bone). Hover over the categories to see all the different material types Nature uses.
Biological structures often perform multiple functions: we define the function of a tessellation based on available scientific information, but also personal observations and deduction. Keep in mind that science may not know a tessellation’s function yet...
A tile with only ‘small’ internal angles (<180° vertex angles); can be a ‘polygonal’ or ‘non-polygonal’ tile.
A tile with at least one ‘large’ internal angle (a vertex angle >180°), as occurs when a tile has an angular process jutting off of one side; can be a ‘polygonal’ or ‘non-polygonal’ tile.
A geometric tile with pointed corners; can be a ‘simple’ or ‘complex’ tile.
A tile with undulating or rounded edges, lacking pointed corners; can be a ‘simple’ or ‘complex’ tile.
Non-overlapping tessellations where tile edges are in direct contact, abutting but not interlocking.
Adjacent tiles overlap each other. This is common for scaled skins, as in fishes and snakes, where plate-like scales protrude from the surface and partially extend over each other. Overlapping tiles are usually thin and flat.
An edge-to-edge interaction between complex tile shapes, as seen in jigsaw puzzles. To achieve this behaviour, tile edges must show a mutual shape dependency, where the edge shape of one tile is the “negative” of the other.
Tiles separated from one another, generally with a visible gap between them (sometimes filled with joint material).
The surface is covered with more than 100 tiles (i.e. you would never try to count them by eye).
The surface is covered with between 10 and 100 tiles (i.e. you could count them, but you wouldn't be happy).
The surface is covered with fewer than 10 tiles (i.e. you are easily able to count them).
A gradual shift from one grain to another.
The tessellation is a symmetrical and therefore predictable pattern, based on a regular base grid.
Strip tessellations arranged along just one axis.
A tessellation without symmetry, formal arrangement or continuity, mostly comprising irregular tile shapes.
Matrix tessellations arranged along two axes.
The coding here is more of an informed guess, as there is no scientific reference available to us for confirmation. If you do have one, please let us know via mail.
Supports the body, acts as a base for muscles and tendons.
Shields the body from external forces, as with armors.
Creates adhesion or friction to improve grip.
Involved in a sensory behavior, as in light or infrared sensors.
Regulating flux between inside and outside, e.g. of water, gas, heat.
Aids in mobility or movement. with movement of Individual tiles translating to larger deformations of the overall structure (e.g. in armored animals that roll their bodies).
Controls the optical appearance of the structure or organism by reflecting or refracting light
The coding is an informed guess, there are no scientific references available for confirmation. If you know of one, please write us a mail!
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