Tilting at Windmills

Before you scroll down, I want to ask you a question – Is this a pattern?

You may think this is a totally pointless question. Try showing it to other people and see if their answer is the same as yours. You might be surprised.

It doesn’t matter where we take this, or what the age or understanding of a group might be, we can ask that one simple question and arguments begin. There will always be many who land firmly on one side of the fence and can’t understand why there should be anyone on the other side. The discussions can get quite animated.

Tilting at Windmills is made entirely from squares that are navy on one side and some shade of pink/purple on the other. They had to be in the correct orientation but the choice of squares was mostly random. However, in a few areas, the colours were carefully chosen to give a hint of a repeated pattern. This had to be enough for the brain to think it was looking for a pattern but quickly be able to dispel the idea. It was deliberately confusing.

If the photo is recoloured I’m sure everyone would agree that it is a pattern. Before you scroll down look at the photo below, or the one at the top, and think about what you can see.

Did you see windmills, or pinwheels? Many people do.
If you didn’t see them before, can you see them now? Are they light or dark? Which way are they turning?

You might have seen, butterflies, bow ties, ‘diamonds’, lozenges, small squares, large squares. or many other different things. (One ten-year old once told us there were diaboloes.) The more you look the more you will see.

The first time we saw groups arguing it came as a bit of a shock. It became apparent that those who declared that it was a pattern were not taking notice of the colours at all. The shapes made a pattern and that was all that mattered. On the other side were those who insisted that if the colours were wrong it couldn’t possibly be a pattern. It certainly justified our arguments for not using colours in our Woolly Thoughts book though we had not been prepared for the extreme reaction whenever a group of people look at the hanging.

This has implications for normal classroom teaching. Almost every teacher provides pupils with coloured shapes for particular tasks but we rarely make it clear whether the colours are strictly relevant to the task. Perhaps those pupils who struggle are not seeing the task as we intended it to be.

Before you scroll down – can you see any tunnels?

We haven’t put this in front of a group for a long time but last week we had a visitor who came to look at what we do so we asked her the usual questions.

I have been looking at this for over 20 years now and I saw something I had never seen before. It might have been the effect of the light at that moment but I suddenly saw three tunnels. The really strange thing is that their outlines do not follow the lines in the divisions of the squares.

It troubled Steve that the inside/outside parts of the tunnels were ‘wrong’. He couldn’t accept them as tunnels but to me they very definitely were. I can see another tunnel above these and one below but they are not as well-defined. There is always something new to be discovered.

Just in case you were struggling to see windmills going in opposite directions, this photo might make them more obvious.

If you want to make your own you can buy the pattern.

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