#
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.

**Back to Chaos and Order**

**Back to Introduction**