Fractals as a field of study did not exist till the 17th century. However, there were some mathematical ideas and concepts developed during that time that can be related to fractals.
One of these concepts was the idea of self-similarity, which is a key characteristic of fractals. In the 17th century, the philosopher and mathematician Gottfried Wilhelm Leibniz introduced the idea of "recurvatio," which he described as the self-similar repetition of a curve at smaller and smaller scales. This concept of self-similarity was further developed by mathematicians in the 18th and 19th centuries, including Karl Weierstrass and Georg Cantor.
A mathematical idea from the 17th century that can be related to fractals is the idea of infinite divisibility. In his book "The Geometry," the French mathematician and philosopher René Descartes introduced the idea of dividing a line into infinitely many parts. This idea of infinite divisibility laid the foundation for later mathematical concepts such as the Cantor set, which is a classic example of a fractal.
While fractals as a formal field of study did not emerge until the 20th century, the ideas and concepts developed in the 17th century and later periods helped to pave the way for the development of fractal geometry.
The most important scientists and artists who have contributed to the development of fractal theory and practice. We will talk more about each of them in the future.
Benoit Mandelbrot - often referred to as the "father of fractals," Mandelbrot was a mathematician who pioneered the study of fractal geometry in the 1960s and 1970s. He is best known for his work on the Mandelbrot set and his book "The Fractal Geometry of Nature."
Felix Hausdorff - who developed the concept of fractal geometry which set out to unify traditional Euclidean geometry with observational properties from nature.
Georg Cantor - a German mathematician who developed the theory of infinite sets, which is foundational to the study of fractals and self-similarity.
Gaston Julia - a French mathematician who worked on the Julia set, which is closely related to the Mandelbrot set.
Helge von Koch - a Swedish mathematician who developed the Koch curve, which is one of the earliest and most famous fractals.
Paul Lévy - a French mathematician who worked on stochastic processes and probability theory, which are related to the study of fractals.
Michael Barnsley - an English mathematician who developed the Iterated Function System (IFS), a technique for generating fractals.
Clifford Pickover - an American mathematician and author who has written extensively on fractals and their applications in science and art.
Jackson Pollock - an American artist who is known for his abstract expressionist paintings, which have been shown to exhibit fractal-like properties.
Roger Penrose - a British mathematician who developed the Penrose tiling, which is a non-periodic pattern that exhibits self-similarity.
“Mandelbulb” - a pseudonym used by a group of artists and programmers who developed a 3D version of the Mandelbrot set, which has become a popular subject for digital art and animation.
