Fractals Minus the Maths
Can we explain fractals without using mathematics? Well, almost.
The Mandelbrot set is the most famous of all fractals. This description of the process of generating the Mandelbrot set avoids using mathematical terminology in so far as this is possible.
We want to know whether each candidate complex number lies in the Mandelbrot set, which is an area of the plane. To find out, we start with the number we are testing, which is the first result. We square this result and then add the number we are testing to it, giving the second result. We square the new result and then add to it the number we are testing. We repeat this process, at each step testing whether the result we get is larger than two. The size of a complex number is its distance from the origin of the plane. If the size of the result is larger than two, then the candidate number is not part of the Mandelbrot set. If after a set number of repetitions, the result we get is still smaller than two then the candidate number is in the Mandelbrot set. Note that a complex number is a pair of numbers giving the horizontal and vertical position of a point.
Compare the above with the standard definition below:The Mandelbrot set is the most famous of all fractals. This description of the process of generating the Mandelbrot set avoids using mathematical terminology in so far as this is possible.
We want to know whether each candidate complex number lies in the Mandelbrot set, which is an area of the plane. To find out, we start with the number we are testing, which is the first result. We square this result and then add the number we are testing to it, giving the second result. We square the new result and then add to it the number we are testing. We repeat this process, at each step testing whether the result we get is larger than two. The size of a complex number is its distance from the origin of the plane. If the size of the result is larger than two, then the candidate number is not part of the Mandelbrot set. If after a set number of repetitions, the result we get is still smaller than two then the candidate number is in the Mandelbrot set. Note that a complex number is a pair of numbers giving the horizontal and vertical position of a point.
The Mandelbrot set is a set of points c, in the complex plane for which the iteration of the function zn+1 = zn2 + c, starting with z0 = 0, remains bounded. That is, a complex number, c, is in the Mandelbrot set if, when starting with z0 = 0 and applying the iteration indefinitely, the absolute value of zn never exceeds a certain number (that number depends on c) however large n gets.