A good novel can often elicit from a reader strong sentiments similar to the moods, feelings, and attitudes depicted in the novel. With the rapid progress in AI, sentiment-based arcs in novels can now be reliably extracted and used to summarize the novel’s plot in the story arc. Are there salient mathematical properties that underlie such story arcs and have far-reaching implications in the writing, adaptation, and reading of the novel? To gain insights into this question, we employ multifractal theory to characterize the narrative coherence and dynamic evolution of sentiments of the novel, Never Let Me Go, by Kazuo Ishiguro, the winner of the 2017 Nobel Prize for Literature as an example. Three methods are compared for fractal scaling analysis, the classic variance-time method, an improvement of the variance-time relation based on adaptive filtering, and adaptive fractal analysis. We find that while variance-time relation fails to accurately extract the fractal scaling exponent, adaptive fractal analysis succeeds in fully characterizing the fractal variations in the sentiment dynamics. The finding may be indicative of the potential that multifractal theory has for computational narratology and large-scale literary analysis, especially for inferring the degree of narrative coherence and variation of the plot of a novel.

一部好小说通常会引起读者强烈的情绪，类似于小说中描述的情绪，感觉和态度。随着AI的飞速发展，小说中基于情感的弧线现在可以可靠地提取出来，并用于总结小说在故事弧线中的情节。是否有显着的数学性质构成此类故事弧的基础，并在小说的写作，改编和阅读中产生深远的影响？为了深入了解这个问题，我们运用多重分形理论来刻画小说《永不放手》的叙事连贯性和动态演变。以2017年诺贝尔文学奖获得者石黑一夫（Kazuo Ishiguro）为例。比较了三种方法的分形标度分析，经典方差-时间方法，基于自适应滤波的方差-时间关系的改进以及自适应分形分析。我们发现，虽然方差与时间的关系不能准确地提取分形比例指数，但自适应分形分析却可以成功地表征情绪动态中的分形变化。这一发现可能预示着多重分形理论对于计算叙事学和大规模文学分析的潜力，特别是对于推断小说的叙事连贯程度和情节变化的潜力。