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In my head, the Ising model is basically all about peer pressure. You're a tiny creature and you live in a little world where you can only be one of two things, up/down, left/right, in/out doesn't matter.
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But what does matter is that you're doing the same thing as you're neighbours. We're going to visualise this with images like the above, representing the two different camps, though at the moment what I've plotted is random, there's no peer pressure going on yet.
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The way that a physicist would quantify this peer pressure is to assign a number to each state, lower numbers meaning more of the little creatures are doing the same thing as their neighbours. We'll call this the Energy, because physicists always call things Energy, that's just what we do.
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To calculate the energy what we're gonna do is look at all the pixels/creatures, and for each one, we look at the four neighbours to the N/E/S/W, everytime we find a neighbour that agrees, we'll subtract 1 from our total and every time we find neighbours that disagree we'll add 1 to our total. Creatures at the edges will simply have fewer neighbours to worry about.
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I'll show you what the equation for this looks like, but don't worry to much about it, the word description should be enough to write some code. If we assign the ith creature the label $s_i = \pm1$ then the energy is
-$$E = \sum_{(i,j)} s_i s_j$$
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Ok let's do some little tests, let's make the all up, all down and random state and see if we can compute their energies.
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