Answer
Fractal is a non-regular geometric shape which has same degree of non-regularity on all scales.The two properties of fractals are self-similarity and the non- integer dimension.
Work Step by Step
Fractal is a non-regular geometric shape which has same degree of non-regularity on all scales. In other words, one can say that fractals are the shapes that one sees in nature.
The geometry that deals with the making of the shapes of the form described above is known as Fractal geometry.
The two properties of fractals are self-similarity and the non- integer dimension. The self-similarity means that if the smaller part of fractal object is magnified many times, then after every step, the same shape will come.
For example, take a leaf of fern. Now, notice that every little leaf is part of the bigger one. And it has the same shape as the whole fern leaf.
It is harder to explain the non-integral dimension. Take example of classical geometry that deals with things of integer dimensions like zero dimensional points, one dimensional lines and arc. 2-D figures like a rectangle and triangle, and 3-D objects such as cuboid and cylinder. Although, there are many natural phenomena,having dimension between these two whole numbers.
Dimension of straight line is one, although a dimension of fractal curve is between one and two. It also depends on space it takes to twist and bend. The more flat the fractal fills a plane, the closer it will approach to two dimensions. Similarly, a "hilly fractal scene" will go to a dimension somewhere between two and three.
