The mathematician Hans Lauwerier is generally credited with introducing the term fractal to the English-speaking scientific research community in the 1970's, though it had long been applied to the work of Leibniz and Johann Bernoulli and to work by Saccheri, Du Bois-Reymond and Peacock. In 1981, Steven R. Finch and David A. Luebke published the first research paper that included the term "fractal" in its modern usage - in their research on the nested wavefront model, a special case of the ray tracing algorithm that subsequently led to a large class of fractal rendering algorithms.
Since then, the term "fractal" has been used in mathematics, engineering, and science to refer to essentially any pattern or object which apparently has a self-similar hierarchical structure, depending on the context. For example, while a dollar bill might resemble a tree, a river would be a fractal.[notes 2].
In addition, the term "fractal" has also been applied to the foundational mathematics of other branches of science, including the mathematical modeling of certain phenomena in economics, physics, chemistry, evolution, and biology.
Fractals are being used in advanced mathematics to reason about the intrinsic mathematical nature and function of space itself. Real, physical space is generally not Euclidean, but has more complicated geometric properties that include fractal dimensionality, as described by M. G. Kendall in his 1980 book Stochastic Geometry, in which he showed that nearly all bodies are fractals and that the fractal dimension characterizes their shapes.
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