Computer Graphics Fractals - Computer Graphics

What are Fractals?

Using a single formula a very complex picture is generated which are known as Fractals, discovered by French/American mathematician Dr Benoit Mandelbrot. Iterations are used for creating Fractals by repeating the formula with different values again and again by considering all the results of previous iterations.

Fractals are used in different areas such as:

• Astronomy – The galaxies, rings of Saturn are analyzed.
• Biology/Chemistry – The bacteria culture, chemical reactions, human anatomy, molecules and plants are depicted.
• Others – Clouds, coastline and borderlines, data compression, diffusion, economy, landscapes are depicted. How Fractals are generated?

When the same shape is repeated again and again as shown below, Fractals are generated. An equilateral triangle is shown in figure a and the repeat ion of the triangle leading to star-like shape is shown in figure b. A new shape is created in figure c by repeating the star-like shape of figure b.

A desired shape can be created by doing unlimited number if iterations. Such shapes are created by using recursion. What are Geometric Fractals?

The shapes that do not have any non-integer or fractal dimension, found in the nature are dealt with the Geometric fractals. A deterministic self-similar fractal is geometrically constructed by starting with the given geometric shape termed as initiator. The initiator subparts are replaced with the pattern, termed as generator. For instance, the initiator and generator from the above figure is used for constructing good patterns. At each step four equal-length line segments replace each of the straight-line segments of the initiator. The scaling factor is 1/3, so the fractal dimension is D = ln 4/ln 3 ≈ 1.2619.

Also, the length of each line segment in the initiator increases by a factor of 4/3 at each step, the length of the curve turns to be infinity as the curve is added with more detail. Computer Graphics Topics