**Preface**

This post — short retelling of this video in English.

If there is no time to read — a living example here. In the field of factor it is possible to substitute any non-negative values. My darlings — 51, 99, 106, 134, 150.

If there is no time to read — a living example here. In the field of factor it is possible to substitute any non-negative values. My darlings — 51, 99, 106, 134, 150.

The mathematics never ceases to surprise with the beauty. This post how to turn such simple operation as multiplication into something surprising. Now answer a question — that the general between it pictures?

All of them are created by means of only one operation — multiplication (actually, still takings of a remaining balance). How so, they look such difficult and different?

The algorithm is quite simple — we will draw around N points at identical distance from each other. The more points, the end result will be richer and brighter. In examples of N = 200. Them we will designate all numbers from 0 to N-1. Farther we will select any non-negative number (now for simplicity we will take natural). Start up it will be 2. Now for each point we will make so — we will take number which we designated it and we will increase on 2. New number от 0 до 2(N-1) will turn out. This number will designate other point to which we will connect the line this. The point 0 will be connected to itself, a point 1 to a point 2, a point 2 with 4, 3 with 6, etc. So we will be at the end of the resources with number 100. Having increased 100 on 2 we will receive 200 — and points with such number at us and is not present. The most logical that can be made — to take the turned-out number on the module N, i.e. in our case 200 and to receive 0. Means the 100th point we connect with 0.

As a result at us such figure still called by a cardioid because of its similarity with the image of heart will turn out.

Now it is possible to select any numbers from 0 to N (after N figures begin to repeat) and to look at result. What to do if we selected fractional number? The answer is simple — to round after multiplication result too down. Thereof at the choice of numbers 2.1 and 2.2 of a figure will almost not differ, however at further increase (2.3, 2.4, 2.5 … 2.9) will resemble more and more the figure received at the choice of number 3. Thanks to it the effect of animation which you can observe in [an interactive example] (http://codepen.io/missingdays/pen/MKJjxB) is created, having exposed factor on 2 (number by which we multiply) and speed at 0:02 (value which increases to factor each frame).

At the choice of factor = 3

You share your interesting factor'ami. Thanks!

This article is a translation of the original post at habrahabr.ru/post/274471/

If you have any questions regarding the material covered in the article above, please, contact the original author of the post.

If you have any complaints about this article or you want this article to be deleted, please, drop an email here: sysmagazine.com@gmail.com.We believe that the knowledge, which is available at the most popular Russian IT blog habrahabr.ru, should be accessed by everyone, even though it is poorly translated.

Shared knowledge makes the world better.

Best wishes.