The Maths of Crowds ๐Ÿ‘ฉโ€๐Ÿ‘ฉโ€๐Ÿ‘งโ€๐Ÿ‘ฆ๐Ÿ‘จโ€๐Ÿ‘ฉโ€๐Ÿ‘งโ€๐Ÿ‘ง๐Ÿ‘จโ€๐Ÿ‘จโ€๐Ÿ‘งโ€๐Ÿ‘ง๐Ÿ‘จโ€๐Ÿ‘จโ€๐Ÿ‘ฆโ€๐Ÿ‘ฆ๐Ÿ‘ฉโ€๐Ÿ‘ฆโ€๐Ÿ‘ฆ๐Ÿ‘จโ€๐Ÿ‘ฉโ€๐Ÿ‘ง

You may think that, given a large number of people in a crowd, it is impossible to know how these people will move. Everyone has free will right?! and so we couldn’t possibly know what will happen. Well people are more predictable than you may know. By coming up with some basic behaviours that people are assumed to follow, mathematical equations have been made to predict the motion of people in crowds.๐Ÿ™Œ๐Ÿป So lets imagine a situation – how about you are simply shopping in a busy town centre like the one in the image. We are assumed to follow these general behaviours:

1: People have a target place that they want to get to (your favourite shop might have a sale on!๐Ÿ‘€๐Ÿƒ๐Ÿผโ€โ™‚๏ธ๐Ÿ‘›๐Ÿ›)

2: There is some randomness in the way people move (would be pretty hard to walk in a completely straight line with lots of people around)

3: People can’t walk through obstacles like walls (unfortunately ๐Ÿ˜ค)

4: People that are with people they know will want to walk close to them (most people like to talk to the people that they go shopping with ๐Ÿ‘ซ)

5: People won’t want to get too close to strangers (can be a little awkward and uncomfortable ๐Ÿ˜ณ)

Using these behaviours, in what is called an Agent Based Model, can be important in ensuring safety in crowd situations. Overcrowding is exteremely dangerous and can lead to serious injury. These models are used in many situations where you might expect lots of people (such as at a football match or in the London underground) in order to ensure the design of the space is safe for that number of people.

Similar models have also been made to explain the movement of a flock of birds ๐Ÿฆ… ๐Ÿฆ… ๐Ÿฆ… or a shoal of fish ๐ŸŸ ๐ŸŸ ๐ŸŸ . Though I don’t think birds (or fish for that matter) are keen shoppers, rules they may follow are not too different. For example they want to fly close to each other to stay in the flock but not too close so they can avoid a crash.

#matharoundus#usingmaths#appliedmathematics#collectivebehavior#crowds#shoaloffish#flockofbirds#modelling#agentbasedmodeling#crowdsafety#stem#scicomm#keeplearning

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