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!
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