The historical backdrop of describing natural objects by mathematics, with respect to Euclidean geometry, is as old as the advent of science itself. In our intuitive understanding, traditionally lines, squares, rectangles, circles, spheres, and so forth have been the fundamental shapes of geometry. Mathematics is mostly concerned with these fundamental shapes to model or approximate or often analyze the natural phenomena. Indeed, nature is not confined to such Euclidean entities that are typically characterized only by integer dimensions, but we restricted ourselves to integer dimensions only. Actually, even now in the beginning phase of our teaching, we discover that objects which have just length are one dimensional, objects with length and width are two dimensional, and those that have length, width, and breadth are three dimensional. Did we ever raise the question for what reason we are always moving toward integer dimension? The response as far as we could possibly know is Never. We never addressed such a question, if there exist objects with non-integer dimensions. However, one person did and he was none other than Benoit B. Mandelbrot. He included another word in the scientific jargon through his inventive work which he termed as a fractal. He was bewildered with such thoughts for many years and realized that nature is not restricted to Euclidean or integer-dimensional space. Rather, a large portion of the natural objects which we see around us are complex in shape, and traditional Euclidean geometry is not adequate to depict them. The notion of fractal geometry has all the earmarks of being irreplaceable for portraying such complex structure at least quantitatively. Mandelbrot has revolutionized Euclidean geometry with the notion of a fractal that has generated extensive attention in almost every branch of science. He presented his new concept through his amazing book “The fractal geometry of nature ”in a striking manner and since then it stayed as the standard reference book for both amateurs and scientists [1]. In a sense, the idea of a fractal has brought numerous apparently disconnected subjects under one umbrella. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.