I am a huge fan of fractals. It is on my top 3 favorite mathematics theory ever. Thus, I am a huge fan of fractal art – such a beautiful way to represent the mathematical theory and rigorous way of representing things. Every time I saw some great artist I shared it with you in any way possible and recently I have been following Killy Thirsk on Instagram and I find his images absolutely incredible. Here are some of his pieces of art and a little bit of fractal theory to go with it :
The mathematics behind fractals began to take shape in the 17th century when the mathematician and philosopher Gottfried Leibniz pondered recursive self-similarity (although he made the mistake of thinking that only the straight line was self-similar in this sense). In his writings, Leibniz used the term “fractional exponents”, but lamented that “Geometry” did not yet know of them.
Fractals, as mathematical equations, are “nowhere differentiable”. In a concrete sense, this means fractals cannot be measured in traditional ways. To elaborate, in trying to find the length of a wavy non-fractal curve, one could find straight segments of some measuring tool small enough to lay end to end over the waves, where the pieces could get small enough to be considered to conform to the curve in the normal manner of measuring with a tape measure. But in measuring a wavy fractal curve, one would never find a small enough straight segment to conform to the curve, because the wavy pattern would always re-appear, albeit at a smaller size, essentially pulling a little more of the tape measure into the total length measured each time one attempted to fit it tighter and tighter to the curve. This is perhaps counter-intuitive, but it is how fractals behave.
Source: photos – Instagram (@killythirsk); maths theory – Wikipedia;
For those interested in more about the mathematics behind fractals, here are some really good books I recommend for different levels and tastes:
Hope you enjoyed this small post of fractal art&theory. Let me know what is your favorite mathematical fact about fractals. Also if you know of any other great artists that do this kind of art, please let me know about them.
Thank you all for supporting me during this time and for finding the time to look to my ideas. Have a great weekend. You can find me on Facebook, Tumblr, Google+, Twitter, Instagram, Lettrs and WeHeartIt. I will try to post there as often as possible.
Don’t forget that maths is everywhere! Enjoy! ~LThMath~