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IBM Journal of Research and Development  
Volume 27, Number 2, Page 164 (1983)
Constrained Channel Coding
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Fractal Nature of Software-Cache Interaction

by J. Voldman, B. Mandelbrot, L. W. Hoevel, J. Knight, P. Rosenfeld
This paper uses fractals to model the clustering of cache misses. The clustering of cache misses can be quantified by a single number analog to a fractional dimension, and we are intrigued by the possibility that this number can be used as a measure of software complexity. The essential intuition is that cache misses are a direct reflection of changes in locality of reference, and that complex software requires more frequent (and larger) changes in this locality than simple software. The cluster dimension provides a measure (and perhaps the basis for a model) of the intrinsic differences between workloads. In this paper, we focus on cache miss activity as a discriminate between interactive and batch environments.
Related Subjects: Analytical models; Fractals; Mathematics (applied); Performance analysis; Storage hierarchies