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Get a daily digest of the latest news in tech, science, and technology, delivered right to your mailbox. Subscribe now.In particular, it deals with dynamic systems, which are highly sensitive to initial conditions.A butterfly flaps its wings in Brazil, and it sets in motion a series of events that eventually lead to a hurricane in Texas.
As Edward Lorenz, who first proposed what became commonly known as the Butterfly Effect, eloquently said, "Chaos: When the present determines the future, but the approximate present does not approximately determine the future."predictions are generally accurate. However, as we move further away in time, more variables come into play, making it more and more difficult to predict the weather with any degree of accuracy.
Returning to Lorenz, his work on weather modeling led to the elucidation of what is called the Lorenz system. This is a system of ordinary differential equations which have chaotic solutions for certain parameter values and initial conditions. In particular, the Lorenz attractor is a set of chaotic solutions of the Lorenz system.
Fractals are often generated through iterative processes. A simple geometric shape or equation is repeatedly applied, each time creating a smaller version of the previous iteration. This iterative generation contributes to their self-similarity.The Mandelbrot set is a captivating and famous fractal that has become somewhat of an icon in the world of mathematics and computer-generated art. The set is named after Benoit B. Mandelbrot, a mathematician at the IBM Thomas J. Watson Research Center.
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