A kaleidoscope as a cyberworld and its animation: linear architecture and modeling based on an incrementally modular abstraction hierarchy

An incrementally modular abstraction hierarchy is known to effectively linearize cyberworlds and virtual worlds which are combinatorially exploding and hardly managed. It climbs down from general level to specific model preserving the higher level modules as invariants. It not only prevents the combinatorial explosion but also benefits the reuse, development, testing and validation of cyberworld resources. By applying this incrementally modular abstraction hierarchy to a kaleidoscope animation, its architecture and modeling is also specified in this paper as a typical case of cyberworlds. In particular, a homotopy lifting property and a homotopy extension property, which satisfy a duality relation, are also described to show how a kaleidoscope world is systematically created top-down from the whole system and bottom-up from the components.