caustics
Caustic (optics)
Caustics made by the surface of water.
In optics, a caustic is the envelope of light rays reflected or refracted by a curved surface or object, or the projection of that envelope of rays on another surface. The caustic is a curve or surface to which each of the light rays is tangent, defining a boundary of an envelope of rays as a curve of concentrated light.
Hiding Images in Plain Sight
An Article by Matt FerraroI recently made a physical object that defies all intuition. It's a square of acrylic, smooth on both sides, totally transparent. A tiny window.
But it has the magic property that if you shine a flashlight on it, it forms an image.
Caustic Engineering
An Article by Geoff ManaughA piece of milled plexiglass acting as a projecting lens; via the Computer Graphics and Geometry Lab at the École Polytechnique Fédérale de Lausanne
New milling techniques applied to glass and plexiglass panels could be used to “create windows that are also cryptic projectors, summoning ghostly images from sunlight.”
[Pauly and Bompas] hope that the technique will be used in architectural design, to create windows that mould sunlight and throw images or patterns onto walls or floors,” which, if timed, milled, and manipulated just right, could produce a slowly animated sequence of images being projected by an otherwise empty window during different times of day.
Architectural Caustics
A Research PaperTo control the shape of a caustic pattern generated by a specular or refractive surface, we need to solve the inverse problem: how can we change the surface geometry, such that incident light is redirected to produce a desired caustic image?
The Tiling Patterns of Sebastien Truchet and the Topology of Structural Hierarchy
A pattern of tiles illustrated by Douat in 1722.
A translation is given of Truchet's 1704 paper showing that an infinity of patterns can be generated by the assembly of a single half—colored tile in various orientations.
Separation and connection in all things
Truchet's approach was more topological than geometric, and the qualitative aspects of pattern take priority over the metric ones. His principles provide a kind of metaphor for the hierarchy of separation and connection in all things.
Corpuscles of nothing and atoms of something
The structure of matter devolved ultimately into the intimate coexistence of something like corpuscles of nothing and atoms of something, segregating through the accidents of history to yield regions differing in density intimately interwoven on different scales. The experience of the world as well as human perception and analysis of any part of it is a matter of the angular scale of resolution and of the time necessary for making comparison between the different parts.
Without such variations and without time to compare remembrances of them, nothing can be experiences.
The scale of resolution determines what is seen
The patterns of Truchet's tiles appear at first glance as variously shaped interlocked regions of black and white, the boundaries between the square tiles being submerged whenever the two regions flanking them have the same color, just as in a real floor the air or cement between the tile edges is not perceived—until one looks closely. The scale of resolution determines what is seen.
This is history
It is easy to see how rapidly diversity is developed by the aggregation of the simplest local choices of direction. This is history.