[This is a work in progress, some interactives might not work]
Prologue
It is a widely known scientific fact that a cow is a sphere. Further, one might trivially observe that, a sphere is a point. Hence, points are the infimum of world models, earning their canonical reverence by representing any object and describing any phenomenon. So, we have much incentive in studying points and the arrangements of points.
Part 0
The Point
The point is the only geometry in the lowest dimension. The complication of dimensions allows us to make lines, squares, cubes, tesseracts, and so on. But since each of those objects can be discretized into the simpler forms – cubes made of squares, square of lines, and ultimately lines made of points, we can see that points truly can be thought of as building blocks of everything.
Kusama was right on money when she said “With just one polka dot, nothing can be achieved”. Points are interesting when they play with each other. In this post, I want to explore how points come together to create a complex myriad of patterns and phenomenon that we see in the world.
Part I
Entropy
Let’s begin where the worlds end – the state of highest entropy or pure randomness! What does it look like to randomly sample points from a Uniform Distribution Function for our dots?
| Number of Points |
One might think "What's in a randomly scattered set of points?" – Quite a bit actually! For instance, Monte Carlo method to Calculate π
Finding pi, etc.
Part II
Patterns
Patterns such as these, while are pleasing to look at, are useful in finding packing etc.
are all too predictable. Let's now try to hit a soft spot between the extremes of disorderliness and orderliness.
