Fractal Geometry History

Fractals had been observed by mathematicians before Bentley took his first photograph, but fractals did not receive their name and definition until the next century. "The concepts behind fractal geometry were first considered by mathematicians during the late 19th and early 20th centuries but at that time were considered too complicated to investigate deeply. It was the later advancement of computers that eventually made the mathematical exploration of fractals possible"₇. It was not until the late 1900's that fractals were explored fully and given their name. Benoit Mandelbrot is known to be the founding father of Fractal Geometry. "During the 1970's, Makdelbrot's research examined unusual or chaotic patterns of behavior in geometric shapes. In 1975 Mandelbrot coined the term "fractal," from the Latin 'fractus' (meaning fragmented, irregular), as a way to describe the self-similar geometric patterns he had discovered"₄. Mandelbrot's curiosity in fractals originated from observations of objects in nature that were not easily modeled by lines, circles, cones, or spheres. Instead they had a "natural, complicated roughness"₇ that he could not explain.

Mandelbrot derived his concepts of fractals while determining the lenth of the Coast of Brittany, which is a coastline along France. He considered the distance of the coast but in different types of scales or perspectives. The three persectives that he considered were for a human being, a rabbit, and an ant. He found that the length of the coast would be/seem shorter for the human than it would for the rabbit and then much less than that for the ant. This meant that due to the roughness of the coastline, the length was different for different scales. This idea birthed Fractal Geometry.

This video explains more of the basics of Fractal Geometry and Mandelbrot's question (stop at 4:10, the remaining will be discussed later).

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