One Simple Habit - 2.0 Being Fractal

“We are what we repeatedly do. Excellence, then, is not an act, but a habit”. – Aristotle.

Last week, we saw how one simple habit can be cultivated by compounding actions. This week I write about fractals from Mathematical design, which reminds me of the Sierpinski Triangle. How repeated patterns can create an interesting shape reflective of its original image and what 'being fractal' means in context to habit forming.

The Sierpinski Triangle is a fascinating design in mathematics. It might remind you of the floor tile patterns or repeated patterns used in construction.

Mandelbrot and Waclaw Sierpinski are two mathematicians who made important contributions in the field of fractals. Now let's look at a discovery which was named after the polish mathematician Waclaw Sierpinski, the Sierpinski Triangle.

The Sierpinski Triangle is an extremely interesting geometric construction which may be created using the following steps:

1.    Start with an equilateral triangle, ΔABC, and locate the midpoints of each of the sides of the triangle.

2.    Connect each of the midpoints with a line segment, and remove the triangle you just created.

3.    You now have three equilateral triangles within the original equilateral triangle. Repeat steps 1 and 2 for each of these triangles. This process can be continued indefinitely or until you choose to stop.

Huh! For such a neat looking figure, the Sierpinski Triangle is actually pretty simple to create! Don't let that fool you though! There are some very interesting patterns going on in this seemingly simple construction.

 For starters, the way in which we construct the triangle creates many more triangles, all similar, within the original triangle. Similar triangles are triangles that have the exact same shape and same angle measurements as one another; their only possible difference is size.

 Each time we create these similar triangles within a previous triangle, the newly created triangles are not only similar to the original triangle, but each created triangle has a perimeter that is equal to 1/2 the perimeter of the previous triangle and has an area equal to 1/4 the area of the previous triangle.

Another interesting pattern is that the Sierpinski construction creates a fractal. A fractal is a geometric construction created by repeatedly performing an operation on an object, or shape, over and over again. In this case, the repeated procedure is removing the triangle created by connecting the midpoints of the sides of the previous triangle.

 Also, the Sierpinski Triangle is a self-similar shape. In technical terms, a self-similar shape is a shape that is similar to smaller parts of itself. In terms of the Sierpinski Triangle, the original triangle is similar to all of the triangles created in its construction, so it is self-similar.

“Watch your thoughts, they become your words; watch your words, they become your actions; watch your actions, they become your habits; watch your habits, they become your character; watch your character, it becomes your destiny.” - Lao Tzu

Habit forming tasks should ideally reflect the end goal just like there are many patterns within the Sierpinski Triangle. For starters, the way in which we construct the triangle creates many more triangles, all similar, within the original triangle. Similar triangles are triangles that have the exact same shape and same angle measurements as one another; their only possible difference is size. If I want to run the marathon then I need to create a habit of running everyday but run smaller distances with similar pace and stride. Reflecting to do a task and repeating it the same way again and again gives us the ability to create a powerful habit.

The true power of fractals lies in the fact that their complexity comes from a few simple actions done over and over again. This is the power and beauty of nature. A clump of cells, with enough division, becomes a human being. This is also true for our financial life. By doing a few simple actions over and over again, we will ensure our path to wealth. One simple action done many times leads to powerful results.

Setting intentions and goals is essential to leadership (and life) success. But how do we bring those intentions to fruition? We do it through small simple actions, repeated faithfully, until they become hardwired habits. It’s the good habits that transform dreams into reality. (And, conversely, it can sometimes be a misguided adherence to bad habits that holds us back.) So keep moving towards your loftiest aspirations with gusto and build powerful habits one simple habit at a time. 

Next week, we prick our brains on the Japanese concept of Kaizen, on how we can reset habits.