Spacetime May Have Fractal Properties on a Quantum Scale

(PhysOrg.com) -- Usually, we think of spacetime as being four-dimensional, with three dimensions of space and one dimension of time. However, this Euclidean perspective is just one of many possible multi-dimensional varieties ...

Beautiful math of fractals

(PhysOrg.com) -- What do mountains, broccoli and the stock market have in common? The answer to that question may best be explained by fractals, the branch of geometry that explains irregular shapes and processes, ranging ...

Fractals patterns in a drummer's music

Fractal patterns are profoundly human – at least in music. This is one of the findings of a team headed by researchers from the Max Planck Institute for Dynamics and Self-Organization in Göttingen and Harvard University ...

UQ researchers break the law -- of physics

(PhysOrg.com) -- Two UQ Science researchers have proved two famous physical laws that have been widely used for the past 25 years do not always work.

Finding the simple patterns in a complex world

An ANU mathematician has developed a new way to uncover simple patterns that might underlie apparently complex systems, such as clouds, cracks in materials or the movement of the stockmarket.

Scientists discover fractal pattern in Scotch tape

(PhysOrg.com) -- Clear cellophane tape – which can be found in almost every home in the industrialized world – may seem quite ordinary, but recent research has shown otherwise. In 2008, scientists discovered that, ...

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Fractal

A fractal has been defined as "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole," a property called self-similarity. Roots of the idea of fractals go back to the 17th century, while mathematically rigorous treatment of fractals can be traced back to functions studied by Karl Weierstrass, Georg Cantor and Felix Hausdorff a century later in studying functions that were continuous but not differentiable; however, the term fractal was coined by Benoît Mandelbrot in 1975 and was derived from the Latin frāctus meaning "broken" or "fractured." A mathematical fractal is based on an equation that undergoes iteration, a form of feedback based on recursion. There are several examples of fractals, which are defined as portraying exact self-similarity, quasi self-similarity, or statistical self-similarity. While fractals are a mathematical construct, they are found in nature, which has led to their inclusion in artwork. They are useful in medicine, soil mechanics, seismology, and technical analysis.

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