Benoit Mandelbrot (1924 - 2010): Mathematics meets art
I notice that the inventor/discoverer (take your pick) of fractal geometry, Benoit Mandelbrot, has died. Here is a short article from BBC about it.
Since the invention of perspective and the beginnings of modern anatomical studies in the Renaissance, there has always been a positive relationship between science and math on the one hand, and art on the other, even though they were at times barely on speaking terms. Mandelbrot was a major figure in this regard, although perhaps not intentionally. But I have always loved the imagery that can be created from the now famous Mandelbrot set:
I generated the above image (click on the image to view a larger version of it) with Fractal Explorer, which can be downloaded from the web for free, and can be used to create far more intricate and complex images than the above "quick sketch." Is it math or art or both? Either way, I think it is more beautiful than the work of many a famous abstract painter.
Of course, the noteworthy thing about fractals is that they resemble real things. Any artist who has ever painted something like this fern, or the lichens on the rocks behind it, has in fact indulged in the creation of fractal imagery:
It is also not difficult to see the resemblance between my fractal above, and these dendrite patterns in limestone (crystal dendrites look rather like plant fossils but are in fact just inorganic crystallization patterns):
We tend to associate the idea of geometry with the rather simple shapes that we all encountered in school mathematics classes. Benoit Mandelbrot was one of the first mathematicians to create, as it were, a mathematical description of far more complex shapes, including organic ones. His work also served as inspiration to artists, both traditional and modern.
Since the invention of perspective and the beginnings of modern anatomical studies in the Renaissance, there has always been a positive relationship between science and math on the one hand, and art on the other, even though they were at times barely on speaking terms. Mandelbrot was a major figure in this regard, although perhaps not intentionally. But I have always loved the imagery that can be created from the now famous Mandelbrot set:
I generated the above image (click on the image to view a larger version of it) with Fractal Explorer, which can be downloaded from the web for free, and can be used to create far more intricate and complex images than the above "quick sketch." Is it math or art or both? Either way, I think it is more beautiful than the work of many a famous abstract painter.
Of course, the noteworthy thing about fractals is that they resemble real things. Any artist who has ever painted something like this fern, or the lichens on the rocks behind it, has in fact indulged in the creation of fractal imagery:
It is also not difficult to see the resemblance between my fractal above, and these dendrite patterns in limestone (crystal dendrites look rather like plant fossils but are in fact just inorganic crystallization patterns):
We tend to associate the idea of geometry with the rather simple shapes that we all encountered in school mathematics classes. Benoit Mandelbrot was one of the first mathematicians to create, as it were, a mathematical description of far more complex shapes, including organic ones. His work also served as inspiration to artists, both traditional and modern.