The Universe we reside within is a Fractal Pattern created from the Fibonacci sequence. Fibonacci Numbers are directly and intricately related to another very special math formula that is found all throughout life and the physical universe. This is the Golden Ratio or “Phi” (as it is more commonly known). It is an irrational number who’s decimal place is never-ending, non-repeating and goes on forever and it looks like this. Although, for the most part scientists and academics alike have rounded it off to five decimal places. So, for all intensive purposes the Golden Ratio (or Phi) is 1.61803. 1.6180339887498948482045868343656381177203091798057………to infinity https://youtube/watch?v=QRNhPzk4IYI&list=UU6dmkXFMzyf27KHt4KgRyVA A fractal is a natural phenomenon or a mathematical set that exhibits a repeating pattern that displays at every scale. If the replication is exactly the same at every scale, it is called a self-similar pattern. An example of this is the Menger Sponge.[1] Fractals can also be nearly the same at different levels. This latter pattern is illustrated in Figure 1.[2][3][4][5] Fractals also includes the idea of a detailed pattern that repeats itself.[2]:166; 18[3][6] Fractals are different from other geometric figures because of the way in which they scale. Doubling the edge lengths of a polygon multiplies its area by four, which is two (the ratio of the new to the old side length) raised to the power of two (the dimension of the space the polygon resides in). Likewise, if the radius of a sphere is doubled, its volume scales by eight, which is two (the ratio of the new to the old radius) to the power of three (the dimension that the sphere resides in). But if a fractals one-dimensional lengths are all doubled, the spatial content of the fractal scales by a power of two that is not necessarily an integer.[2] This power is called the fractal dimension of the fractal, and it usually exceeds the fractals topological dimension.[7] As mathematical equations, fractals are usually nowhere differentiable.[2][5][8] An infinite fractal curve can be conceived of as winding through space differently from an ordinary line, still being a 1-dimensional line yet having a fractal dimension indicating it also resembles a surface.[2]:15[7]:48 The mathematical roots of the idea of fractals have been traced throughout the years as a formal path of published works, starting in the 17th century with notions of recursion, then moving through increasingly rigorous mathematical treatment of the concept to the study of continuous but not differentiable functions in the 19th century, and on to the coining of the word fractal in the 20th century with a subsequent burgeoning of interest in fractals and computer-based modelling in the 21st century.[9][10] The term fractal was first used by mathematician Benoît Mandelbrot in 1975. Mandelbrot based it on the Latin frāctus meaning broken or fractured, and used it to extend the concept of theoretical fractional dimensions to geometric patterns in nature.[2]:405[6]
Posted on: Mon, 29 Dec 2014 02:36:00 +0000
Trending Topics
Recently Viewed Topics
© 2015