Make a red and yellow hexahexaflexagon by folding and gluing a multicoloured paper strip, following the algorithm. Once made you start to explore it. As you fold it up and unfold it, you magically reveal new sides as the flexagon changes colour. To explore it fully, you need a map. A graph seems a good representation, which you create as you explore.

A graph is like a tube map, with circles (nodes) for places revealed and lines between them (edges) showing which circles you can move between by folding and unfolding the flexagon. It is a special kind of graph that can be thought of as a machine – a ‘finite state machine’. The nodes of the graph are different states the flexagon can be in and the edges show what actions that can be taken to move between states. It describes the computations involved in flexing the flexagon. A finite state machines is a very useful tools in the computational thinking toolbox. They are an important way for describing what computer systems do.

Learn about:

• graphs
• finite state machines
• specification
• computational thinking
• abstraction
• data representation
• generalisation
• pattern matching
• evaluation and logical thinking

Resources

This session comes with linked booklets/activity sheets that you can download:

• Activity: The HexaHexaFlexagon Automata Activity [PDF] (forthcoming)
• Booklet: Computational Thinking – HexaHexaFlexagon Automata [PDF]

This activity is closely linked to the Tour Guide and the Knight’s Tour Activities.