FRACTALS- A Broken Story

Fractals are fascinating geometrical objects that contains detailing at atomic level and if we understand it. It is nothing but illusion of self repeating loops at the scale of intrensic shapes and design that exist inside and outside of the environment.

Isn't it Heuristic to understand this things and keep your curiosity at top!!

Fractals are distinct from the simple figures of classical, or Euclidean, geometry—the square, the circle, the sphere.

Types of Fractals:

1.koch snowflake

2.Mandelbrot set

3.Dragon curve

4.Hilbert curve

5.Newton Fractal

6.Menger Sponge

Variations of Geometry at Different Fields:

1. The variation in the self repeating loop of the complex yet simple structure that is everywhere around us.
2. Modularity of precision of the geometrical objects that exist in the nature and around us behave differently but esoteric in the sense of understanding them.

Math Behind Structures

1. ?In Euclidean geometry we assign values to an object's length, height and width, and we calculate attributes like area, volume and circumference based on those values.
2. But most objects are not uniform; mountains, for example, have jagged edges. Fractal geometry enables us to more accurately define and measure the complexity of a shape by quantifying how rough its surface is.
3. The jagged edges of that mountain can be expressed mathematically: Enter the fractal dimension, which by definition is larger than or equal to an object's Euclidean (or topological) dimension (D => DT).

D = log N / log (1/h)

1. D?is the dimension,
2. ?N?is the number of grid boxes that contain some part of the fractal inside,
3. ?h?is the number of grid blocks the fractals?

Applications:

1.Astronomy

2.Nature

3.Computer science

4.Applied chemistry

5.Quantum Mechanics

6.nanotechnology

There are some of the areas where it is being used.