Recursively Defined Curves in Computer Graphics

Recursive means repetition that is using the same method or formula on output to create next. Recursively defined curves are created by using the same formula with different values.

Types of Recursively Defined Curves 

1. Koch Curve
2. C Curve
3. Hilbert’s Curve
4. Dragon Curve
5. Fractals

Koch Curves

These curves are also known as snowflakes. It is a fractal curve and has infinite length and with each iteration, the curve length is increased by a factor of 43.

C Curves

C Curve is also known as a self-similar fractal curve. These curves are extensions of cubic curves. These curves are described in the year 1910.

Hilbert’s Curve

It was described in the year 1891. It comes under the category of a space-filling curve. Every point in a square grid is visited with the help of the grid having the power of 2. For example, a grid of size 2×2, 4×4, 8×8, 16×16 can be used.

Dragon Curves

A Dragon curve is a recursive non-intersecting curve also known as the Harter–Heighway dragon or the Jurassic Park dragon curve. The dragon curve can tile the plane. Each edge of a square tiling with a dragon curve is replaced with another possible tiling with the help of the recursive definition of the dragon.

Fractals

Fractals are complex patterns that appear to be identical across different scales. They are created by repeating one simple process multiple times with the help of a loop. A fractal is a never-ending pattern.

Types of Fractals 

• Self-Similar Fractals: These type of fractals appears to be the same in different directions and scale. For example-Model trees, shrubs, and plants.
• Self Affine Fractals: A fractal whose pieces are scaled by different amounts in both directions. These types of fractals appear approximately identical at different scales. For example-Model water, clouds, terrain.
• Invariant Fractals: This class of fractals includes self-squaring fractals.