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So congratulations for making it through this section.

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I hope you liked it.

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I think this section was pretty much different from the other sections because it was really based on

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randomness.

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And I mean, this is the whole idea of Monte Carlo, but also I understand that this can be a bit annoying

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because sometimes you just have to rerun the same simulation over and over again and just see if it

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works or if it doesn't work.

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And then you have to tune some of the parameters or the numbers of steps or iterations that you want

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to do.

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So really, randomness is sometimes difficult to deal with.

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However, it allowed us to really simulate the collective magnetic behavior of this tiny individual

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magnets.

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And if we would have solved this problem using the gradient descent method, we would have never finished

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because it would have taken so much more time.

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So it really is an advantageous technique using this Monte Carlo algorithm.

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However, it also has its downsides.

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And you have to be really careful to use it in the proper way.