spirograph
The Spirograph is a geometric drawing toy that produces mathematical curves known as hypotrochoids and epitrochoids. It was developed by British engineer Denys Fisher. Drawing toys based on gears have been around since at least 1908, when The Marvelous Wondergraph was advertised in the Sears catalog. An instrument called a spirograph was invented by the mathematician Bruno Abdank-Abakanowicz between 1881 and 1900 for drawing spirals (see the catalog of the Conservatoire des Artes et Metiers in Paris). Another Frencheman, Bataille, patented such an instrument in March of 1887. Fisher first exhibited the Spirograph in 1965 at the Nuremberg International Toy Fair and produced it in Britain. Kenner, Inc., acquired U.S. distribution rights, introducing it in this country in 1966 as a creative toy for drawing "a million marvelous patterns." The set includes eighteen transparent plastic wheels, two transparent plastic rings, two transparent plastic bars, two ballpoint pens (blue and black), four pins in a plastic case, a thumbtack, a miscellaneous metal piece, and an instructional pamphlet. Most of the pieces fit in a blue storage tray which in turn is in a cardboard box with cover. To draw a desired shape, one must select one of the smaller wheels to be placed within one of the two larger wheels. All wheels have teeth on the edges, like gears, and can be rotated around the larger wheels. Then one puts a pen through one of the small holes on the small wheel and draws on the paper while turning the small wheel around the inner circumference of the large wheel. The rotational motion of the small wheel translates into a pattern that the pen draws on the paper. A small booklet lists various shapes and procedures for drawing them. Every small wheel has several holes through which to put a pen point, allowing several different designs per small wheel.
hexagonal lattice
The hexagonal lattice (sometimes called triangular lattice) is one of the five two-dimensional Bravais lattice types. The symmetry category of the lattice is wallpaper group p6m. The primitive translation vectors of the hexagonal lattice form an angle of 120° and are of equal lengths. Honeycomb point set as a hexagonal lattice with a two-atom basis. The gray rhombus is a primitive cell. The honeycomb point set is a special case of the hexagonal lattice with a two-atom basis. The centers of the hexagons of a honeycomb form a hexagonal lattice, and the honeycomb point set can be seen as the union of two offset hexagonal lattices. In nature, hexagonal patterns often appear. E.g. the skin of reptiles, honeycombs or carbon atoms of the two-dimensional material graphene are arranged in a honeycomb point set.
controls
Overview of the hexClock-player controls:
point count: total number of points (or timesteps) that are drawn
time step: the distance (or time) between two consecutive points
ratio distance: ratio of inner circle to middle circle - responsiple for the extent of the loops
ratio radius: ratio of middle circle to outer circle - responsiple for the number of loops
radius size: size of outer circle - responsible for overall size of the spirograph
initial rotation: direction of spirograph
horizontal cell count: number of cells in horizontal direction
vertical cell count: number of cells in vertical direction
horizontal rule: rhythm for mapping the spirograph points in horizontal direction
vertical rule: rhythm for mapping the spirograph points in vertical direction