In mathematics, Arnold's cat map is a chaotic map from the torus into itself, named after Vladimir Arnold, who demonstrated its effects in the 1960s using an image of a cat, hence the name.
Thinking of the torus as the quotient space
Arnold's cat map is the transformation
given by the formula
Equivalently, in matrix notation, this is
That is, with a unit size equal to the width of the square image, the image is sheared one unit up, then one unit to the right, and all that lies outside that unit square is shifted back by the unit until it's within the square.
The maneki-neko (Japanese: 招き猫, literally "beckoning cat") is a common Japanese figurine (lucky charm, talisman) which is often believed to bring good luck to the owner. In modern times, they are usually made of ceramic or plastic. The figurine depicts a cat (traditionally a calico Japanese Bobtail) beckoning with an upright paw, and is usually displayed—often at the entrance—of shops, restaurants, pachinko parlors, and other businesses. Some of the sculptures are electric or battery-powered and have a slow-moving paw beckoning. The maneki-neko is sometimes also called the welcoming cat, lucky cat, money cat, happy cat, beckoning cat, or fortune cat in English.
Maneki-neko comes in different colors, styles and degrees of ornateness. Common colors are white, black, gold and sometimes red. In addition to ceramic figurines, maneki-neko can be found as keychains, piggy banks, air fresheners, house-plant pots, and miscellaneous ornaments, as well as large statues. It is also sometimes called the "Chinese lucky cat" due to its popularity among Chinese merchants.
George Clark (1888-1946) was a British film actor and film producer during the silent era. For many years Clark worked with the British star Guy Newall, who he had met during the First World War. Together they founded Lucky Cat Films and later George Clark Productions, securing a distribution arrangement with the larger Stoll Pictures.
After initially working out of a studio on Ebury Street in Central London, they raised finance to construct Beaconsfield Studios and work began in 1921. They opened the new studio the following year, but after being hit by the Slump of 1924 remained largely inactive for the rest of the decade. Clark later sold the studios to the British Lion Film Corporation in 1929.