This paper applies the mathematics of chaos to the task of designing indoor rock-climbing routes. Chaotic variation has been used to great advantage on music and dance, but the challenges here are quite different, beginning with the representation. We present a formalized system for transcribing rock climbing problems and then describe a variation generator that is designed to support human route-setters in designing new and interesting climbing problems. This variation generator, termed strange beta, uses chaos to introduce novelty. We validated this approach with a large blinded study in a commercial climbing gym, in cooperation with experienced climbers and expert route setters. The results show that strange beta can help a human setter produce routes that are at least as good as, and in some cases better than, those produced in the traditional manner.
As mentioned above, the use of computers in creative tasks---for independent generation and or in assistance roles---is not a new idea. Computation has a particularly rich history in music composition, in both generative and assistant roles @cite_19 . Route setting for indoor climbing is viewed by its practitioners as a creative task on par with music composition, requiring substantial expertise in order to create routes that are both of an appropriate difficulty and interesting to climb. A climbing route is a prescribed sequence of dynamic movements: a sequence of symbols from a complex language not unlike a dance or a tonal music composition, both of which can also be viewed as symbol sequences. All three of these domains---climbing, music, and dance---have strong notions of style,'' but that notion is very hard to formalize, even for experienced practitioners.
@cite_19
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Stylistic composition is a creative musical activity, in which students as well as renowned composers write according to the style of another composer or period. We describe and evaluate two computational models of stylistic composition, called Racchman-Oct2010 (random constrained chain of Markovian nodes, October 2010) and Racchmaninof-Oct2010 (Racchman with inheritance of form). The former is a constrained Markov model, and the latter embeds this model in an analogy based design system. Racchmaninof-Oct2010 applies a pattern discovery algorithm called SIACT and a perceptually validated formula for rating pattern importance, to guide the generation of a new target design from an existing source design. A listening study is reported concerning human judgments of music excerpts that are, to varying degrees, in the style of mazurkas by Frederic Chopin (1810–1849). The listening study acts as an evaluation of the two computational models and a third, benchmark system, called Experiments in Musical Intelligence. Judges’ responses indicate that some aspects of musical style, such as phrasing and rhythm, are being modeled effectively by our algorithms. Judgments are also used to identify areas for future improvements. We discuss the broader implications of this work for the fields of engineering and design, where there is potential to make use of our models of hierarchical repetitive structure.