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WEB GEOMETRY and force vectors based on observations of spider webs. It takes advanced mathematics to even begin to solve the humble spider's ingenuity. https://lnkd.in/dYdY4x3 View in LinkedIn

WIDE VARIATION. "Interestingly, the overall size of different orb webs varies from centimetres to meters, while the ratio of spiral to radial thread diameter varies from ∼0.1 to 1. Concomitantly, the extensibility and elastic modulus of the spiral and radial threads can differ by 1 and 3 orders of magnitude, respectively." https://lnkd.in/d5Wdths View in LinkedIn

POINT FAILURE. "The failure of silk threads occurs at points where the filament is disturbed by that external force, but after failure, the web returns to stability--even in simulations using broad forces, like hurricane-force winds." I have personally observed this. https://lnkd.in/dND28gV View in LinkedIn

SACRIFICIAL FAILURE DESIGN. "When a force strikes the web, such as that from a trapped fly, the web deforms in distinct ways at multiple scales yet fails only where silk threads are under the most stress. The web manages that feat because of slipping that takes place within the spider-silk protein molecules. The result is compensation for some stress, yet sacrificial failure when stress becomes extreme, preserving the web as a whole." https://lnkd.in/dND28gV View in LinkedIn

VORONI DIAGRAMS. https://lnkd.in/dYnv5AY View in LinkedIn

VORONI DIAGRAMS and spider webs. https://lnkd.in/dAawv-v View in LinkedIn

DIRICHLET TESSELLATIONS and spider webs. "Plane pictures of three-dimensional convex polyhedra, plane sections of three-dimensional Dirichlet tessellations, and flat spider webs with tension in all the threads are essentially the same geometric object. At the root of this remarkable coincidence is a single geometric diagram that permits us to offer a unified image of the connections among these and other objects." http://link.springer.com/chapter/10.1007%2F978-0-387-92714-5_18 View in LinkedIn

SHORTCUTS OF THE TIERED WEAVER. "Webs built in unnaturally rapid succession by the same spider (4 in 24 h when 1 is the norm) became sequentially smaller, had fewer radii, shorter capture spirals, and were wider meshed." http://www.sciencedirect.com/science/article/pii/S0031938497001868 View in LinkedIn

SONG OF DARWIN. "The more I study nature, the more I become impressed […] that the contrivances and beautiful adaptations [acquired through natural selection] transcend in an incomparable degree [those] which the most fertile imagination of the most imaginative man could suggest with unlimited time at his disposal." http://www.sciencedirect.com/science/article/pii/S0960982214003881 View in LinkedIn

WEB DESIGN PLASTICITY. "Decreasing temperature from 24° to 12°C caused the capture spiral to have fewer and wider spaced meshes, which did not change overall capture area but reduced the length of capture-spiral threads laid down. Subsequent increase of temperature to 24°C restored the number of meshes laid down, but the wider mesh was retained, causing the capture area to be increased over initial control values." https://lnkd.in/dWUF7eR View in LinkedIn