Journey to Infinity

and what you might find along the way

 

BrainWorks 3

1 If you have seen family trees of ancestors and relations, you'll know that they can spread out rather like a bifurcation diagram. Let's imagine that there's a family where each person married and had two children who both married, and so on. The tree might start something like this:

A larger version of this family tree, without the names, would look very neat and tidy, along these lines:

Notice how crowded it's getting by the 6th generation. The 7th generation would have 128 names, and the 8th would have 256. In other words, if you add a few more generations on the same pattern of two per family, you'll easily find out why the bifurcation fractal looked like a 'mess' as it grew.

Suppose one of the branches of this family had a different characteristic, such as three children in every generation, only two of whom married. You would see a quite different pattern down that branch.

Keep in mind the idea that just one small thing can change a bifurcation from being regular and symmetrical to being irregular and not symmetrical. If this were a real family tree, and there was some sort of regular difference between the two main lines from the top...

What could stay the same down both lines?

What could change down both lines?

What sort of influence, other than marrying someone with a different surname, might create a new form of difference?

2 Here is another enlargement (from a zoom-in of enormous depth) from the Mandelbrot set:

And here is a version I made with my graphics program:

This isn't a bifurcation. Notice that it has:

multiple branches,

self-similar patterns within the branches,

areas around it which seem to enclose it, even influence it, in different ways.

It does not really look like a family tree, but suppose it symbolises a family in another way. It might be a sort of diagram of the way different branches of the family have moved, been influenced, and changed. They are in touch with each other, in some ways, even though they are distant from each other.

Use your logical and factual thinking ability to work out what happens during several generations of a family and its movements and changes. Apply your lateral thinking ability to suggest how this fractal, its lines,directions, patterns, colours and surrounding areas of colour might represent that whole process.

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