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Clever mathematical techniques are the foundation of increasingly realistic computer models and simulations. Now, math research is on the verge of creating tools that mathematicians hope will cut two ways: help scientists unlock explanations to many phenomena that remain mysterious and produce new modeling systems that could revolutionize product development and manufacturing. All this could be coming from fractals, those crinkly lines that look the same no matter how much they're magnified. "Fractal" is the term mathematicians use for patterns that repeat on all scales--like the spikes on a fern leaf that could be tiny copies of the fern itself.

Fresh research indicates that such recurring patterns may be more fundamental in nature than had been thought. If the new insights can be captured in fractal algorithms, science could gain extraordinary new powers. The same basic formulas could be "exploded" in scope to help scientists better understand large-scale systems such as the influence on climate from patterns of sunlight reflecting off the ocean's surface. And they could predict traffic flows on the Internet, or on physical highways. Conversely, "imploding" the formulas would adapt them for small-scale use, such as the behavior of molecules. That could save time in r&d by pointing out which avenues are more promising. Designers and engineers could update near-perfect models to speed their work on new products and processes.