Discontinuous and alternate q-system fractals

Abstract This paper presents various patterns and computer art from three extensions to common fractal methods: Here, I use discontinuous functions (such as Boolean functions and the conditional function), plots of root-finding methods other than Halley's and Newton's methods (such as Aitken's and Muller's methods), and fractals produced using arithmetic in q -systems other than the complex number system. Still fractal images and parametrization “movies” are discussed; these allow several new properties of these algorithms (and their combinations) to be uncovered. Also, the interaction of randomness with fractals is explored.