I know some math. Whenever I come across the word fractals, I see cool colourful pictures. So I googled it and can't understand a word about it in Wikipedia. Can anyone explain me what fractals are in a basic yet clear way?

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    $\begingroup$ What is your current level of knowledge in mathematics? Have you seen basic undergrad topics like calculus and linear algebra, have you seen intermediate/advanced topics like analysis, topology, group theory? This will help in providing some resources to you! $\endgroup$ – Alexander H. R. Mar 5 at 15:19
  • $\begingroup$ I know only a bit of calculus. I have no basic knowledge in other topics you have mentioned.😊 $\endgroup$ – I am Me Mar 5 at 15:24
  • $\begingroup$ Possible duplicate of What exactly are fractals $\endgroup$ – Xander Henderson Mar 5 at 20:00

Fractals are self similar structures with minor changes to the original. The best example is a tree. Say you have the root of a tree, and copy it, but reduce the length by 75% and rotate it 25 degress or something like this. then place it somewhere on the trunk. now you have two branches, you do the same to the second branch so that you get a third branch. Then you repeat this process all over such that you form a tree.

So best way to put it is that if you have some rules, you make copies to the object and change it so that you get some kind of large tree structure with branches that look similar to the original when you zoom in.

  • $\begingroup$ Wow! Exactly what I expected... Thanks a lot! $\endgroup$ – I am Me Mar 5 at 15:33
  • $\begingroup$ No problem. Of course you could read and do some math on fractals. Or use some software where you can change parameters and visualize a fractal. And there are different types of fractals, like mandelbrot (with complex numbers), and IFS, iterated function fractals, there are a whole bunch of different types of fractals. Good luck. $\endgroup$ – Natural Number Guy Mar 5 at 15:36
  • $\begingroup$ To do math on fractals, in which topics should I have a basic knowledge... $\endgroup$ – I am Me Mar 5 at 15:40
  • $\begingroup$ @IamMe I would say that Analysis (Real and Complex) and Topology would be the goal if you are interested in fractals! The notes I linked above provide a good introduction to this, strictly in the context of fractals. The track to this would be to get a solid understanding in Calculus, and then Linear Algebra. Once you have those under your belt, you can learn about introductory real and complex analysis, move on to mathematical analysis and topology for which there are many great references on stackechange. All this is generally taken as part of a Mathematics undergrad program. $\endgroup$ – Alexander H. R. Mar 5 at 15:50
  • $\begingroup$ Im no expert in this field. My guess is, function theory, iterated functions, natural numbers, complex numbers, vector, calculus. And fractals can also be done in binary numbers. I found this: www2.cs.arizona.edu/patterns/weaving/webdocs/mo/H/… $\endgroup$ – Natural Number Guy Mar 5 at 15:52

A great resource for this would be a course at the University of Waterloo by E. R. Vrscay called "Chaos and Fractals". His lecture notes are available free online here. Although a bit more advanced than elementary calculus, his course is self contained and provides excellent explanations of the more advanced topics you might not be familiar with.

Furthermore, this Numberphile video on the The Mandelbrot Set could be particularly enlightening.

  • $\begingroup$ Thanks a lot. I will refer them. $\endgroup$ – I am Me Mar 5 at 15:31

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