I-Corps: Harnessing Chaotic System Variability

这个I-Corps项目的更广泛的影响/商业潜力，需要一种基于混沌系统可变性的技术，是它改变和增强人们在线上和离线与音乐互动的能力。作为音乐变革的推动者，这项拟议中的技术使“个性化音乐”超越了播放列表和歌曲建议。第一次，音乐听众可以把自己的创造力带到他们所关心的歌曲中。该项目引入了一种新的音乐范式，歌曲可以单独或与其他歌曲一起在点击按钮时进行演变和转变。选择音乐作为这项技术的应用是经过深思熟虑的。音乐是一种高度依赖上下文的应用程序，每个音符或音乐事件都是由之前的音符和事件决定的，每个音符或事件都预示着即将到来的音符或事件。这种先进的技术产生的音乐变化既可以分析，也可以用于音乐手段，这表明该方法可以应用于其他依赖于上下文的符号序列，例如定义图像、文本、电影和视频的符号序列。此外，它可以作为一般媒体从业者的创意发生器，并通过将科学与音乐艺术联系起来，激发K-12及以上学生对工程的兴趣。这个I-Corps项目利用混沌系统的可变性来产生一系列与上下文相关的符号的变化，例如那些构成音乐作品的符号。大多数工程师都在寻找消除混沌行为的方法。然而，在其“混沌状态”中，耗散混沌系统由于其解对初始条件的敏感性而具有自然的变异性机制。这种内置的可变性可以通过混沌映射技术加以利用，该技术将有序输入转换为可变有序输出。变体输出可以接近原作，也可以变异得面目全非，也可以在这两个极端之间达到一定程度的变异。该方法包括将输入解析为原始元素{Ni}的有序序列，原始元素按连续整数值i=1,....，imax顺序索引。对于每一个“i”，一个选择算法决定Ni是修改还是替换的候选元素，从而成为一个“受体元素”。然后，替代或修改算法通过用替代元件改变或替换受体元件对其进行操作。由原始的和被替换的或修改过的元素组成的有序的结果集包括变体输出。几乎无限的变化是可能的，每一个都是独一无二的。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The broader impact/commercial potential of this I-Corps project, entailing a technology based on chaotic system variability, is its ability to alter and enhance how people interact with music on and off line. By acting as a musical change agent, the proposed technology takes "personalized music" beyond playlists and song suggestions. For the first time, music listeners can bring their own creativity to the songs they care about. This project introduces a new paradigm for music where songs evolve and undergo transformation alone or with other songs, at the click of a button. The choice of music as an application for the technology is deliberate. Music is a highly context-dependent application where each note or musical event is determined by the preceding notes and events, and each note or event foreshadows those yet to come. That this advanced technique produces musical variations that can be analyzed as well as used for musical means suggest that the methodology could be applied to other sequences of context-dependent symbols, such as those that define image, text, film, and video. Furthermore, it can serve as an idea generator for media practitioners in general, as well as stimulate interest in engineering for students K-12 and beyond by linking science with the musical arts. This I-Corps project harnesses chaotic system variability to generate variations of a sequence of context-dependent symbols, such those that constitute a musical work. Most engineers seek ways to eliminate chaotic behavior. Yet in its "chaotic regime", a dissipative chaotic system possesses a natural mechanism for variability due to the sensitivity of its solutions to initial conditions. This built-in variability can be exploited by a chaotic mapping technique that transforms an ordered input into a variant ordered output. The variant output can be close to the original work, it can mutate beyond recognition, as well as achieve degrees of variability in between these two extremes. The method includes parsing the input into an ordered sequence of original elements {Ni}, the original elements sequentially indexed by successive integer values i=1,....,imax. For each "i", a selection algorithm determines whether Ni is a candidate for modification or replacement, thus becoming a "receptor element". A substitution or modifying algorithm then operates on at least one of the receptor elements by varying or replacing it with a substitution element. The resulting ordered set of original and substituted or modified elements comprises the variant output. A virtually infinite set of variations is possible, each unique.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.