Scott Domes

How simple rules lead to complex patterns

Computing the theory of everything

March 06, 2021

The ultimate goal of physics is finding the Theory of Everything.

This theory would be a single framework that explains all physical aspects of the universe. Right now, we can explain many aspects pretty well. But there’s one major divide.

We have the theory of general relativity, which works very well for big things. We also have the theory of quantum mechanics, which works well for very small things.

But we don’t have a way to combine them.

The Theory of Everything would be a single set of equations that explain all interactions between matter, energy, space, and time.

It would explain the origins of the universe, the orbit of the earth around the sun, and all the weird quantum behaviour we keep uncovering.

When you stop to think about it, this does seem a little crazy. Can a few equations really explain everything?

The universe is mind-blogglingly massive and complex. Can we possibly reduce it all to a bit of math?

Computer scientist Stephen Wolfram says we can, and here’s how.

Wolfram’s emergent complexity

Wolfram has had a busy and storied career in both computer science and physics, but today we’ll focus on just one contribution. Wolfram proved that you can generate complex behaviour from a few simple rules.

Let’s take a grid, like so. The grid is divided into cells, and in the middle of the very top row, one cell is filled in.

If we proceed row by row down the grid (second row, third row, fourth row), we can generate different patterns by following different rules for filling in cells.

Here’s an example rule: if the same cell in the previous row is filled in, we fill it in on the next row. Click Run below to see what pattern this generates.

Not very exciting, is it? But we can use a more interesting rule.

What if we say, if the cell to the left of the cell in the previous row (their left neighbor) is filled in, fill it in on the next row?