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Whole Number Dynamics I

The first of five articles concentrating on whole number dynamics, ideas of general dynamical systems are introduced and seen in concrete cases.

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Whole Number Dynamics II

This article extends the discussions in "Whole number dynamics I". Continuing the proof that, for all starting points, the Happy Number sequence goes into a loop or homes in on a fixed point.

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Whole Number Dynamics III

In this third of five articles we prove that whatever whole number we start with for the Happy Number sequence we will always end up with some set of numbers being repeated over and over again.

Difference Dynamics

Stage: 4 and 5 Challenge Level: Challenge Level:1

 number cycle
Choose any three numbers. The differences between your numbers give you three new numbers. Repeat this operation to give a sequence. In this example the sequence starts: $15, 39, 8 \to 24, 31, 7  \to  7, 24, 17  \to 17, 7, 10 ...$. What happens to this sequence. Investigate for different starting points.
What do you notice? Can you explain what happens?
 
How about sequences starting with four numbers, or two numbers?
 
See the article Difference Dynamics Discussion.