Art and Maths together: Fractals

Thats right. You can use simple mathematics to create beautiful images and art work. There are enough examples in nature for doing so. It is called Fractal.

Basically a Fractal is an image in which some smaller image is repeatedly fitted to create patterns.

See this Triangle Fractal. Basically you are creating patterns by making triangles fit within the triangle.

Now you can use the same technique for a different triangle to create a snowflake. Maths to make drawings of snowflakes – well here you go-

To create a Koch snowflake, one begins with an equilateral triangle and then replaces the middle third of every line segment with a pair of line segments that form an equilateral “bump.” One then performs the same replacement on every line segment of the resulting shape, ad infinitum. With every iteration, the perimeter of this shape increases by one third of the previous length. The Koch snowflake is the result of an infinite number of these iterations, and has an infinite length, while its area remains finite. For this reason, the Koch snowflake and similar constructions were sometimes called “monster curves.” Citation-Wikipedia

Now to create a leaf- see the leaf consists of smaller leafs and smaller leafs.

Hey even nature uses maths here-this is a fractal shape.

is this art- well Jackson Pollock thought so

While Pollock’s paintings appear to be composed of chaotic dripping and splattering, computer analysis has found fractal patterns in his work.^[7]

From wikipedia

Here is the equation-

A fractal is “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,”^[1] a property called self-similarity. Roots of mathematical interest in fractals can be traced back to the late 19th Century; however, the term “fractal” was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning “broken” or “fractured.” A mathematical fractal is based on an equation that undergoes iteration, a form of feedback based on recursion.^[2]

A fractal often has the following features:^[3]

• It has a fine structure at arbitrarily small scales.
• It is too irregular to be easily described in traditional Euclidean geometric language.
• It is self-similar (at least approximately or stochastically).
• It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve).^[4]
• It has a simple and recursive definition.