The fractal is a geometric object that can be divided into parts, each one similar to the original object. It is said that fractals have infinite details, are generally self-similar and scale. In many cases, the fractal can be modified by a standard model, usually a constant or iterative process.
In this case, we present a simple application of fractal geometry for anyone with a smartphone.
Accessing the WhatsApp, I wrote the word Fractal, took a screenshot, sent to myself and took a screenshot of the new screen. I repeated this process 15 times as present in the video below.
Notice how the word Fractal and the purple curves of the first screen of WhatsApp slowly disappear, with each new level of the picture there is a reduction in its dimensions until they do not fit the amount of pixels that the screen of the cell represents when taking a screenshot.
The use of this concept is not only to be beautiful or fun, we can use the idea of reducing consecutive values when we want to show that a series converges to a defined value. For example the series 1/1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 … + 1 / n². In the case of this series, for n infinity, it converges to 2. That is, even if the sum never stops occurring, it will be closer and closer to this value and will never be able to reach it, except when it reaches infinity … if you want to try, write in the wolframalpha.com the expression 1/1+1/2+1/4+…+1/2¹⁰⁰⁰, our if you are lazy click here.
Xoxelho 