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A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?

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LOGO Challenge - the Humble Square

Look at how the pattern is built up - in that way you will know how to break the final pattern down into more manageable pieces.

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LOGO Challenge - the Logic of LOGO

Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?

Schlafli Tessellations

Age 11 to 18 Challenge Level:

Although the three regular tessellation (using squares, triangles and hexagons) are well known, they do pose a demanding challenge in terms of 'elegant' LOGO procedures.

This problem considers the eight semi-regular tessellations, which geometrically are more stimulating and are shown below, along with their respective Schlafli symbols.

Look carefully at each diagram in turn. What is the meaning of the symbols?

The symbols are used in two and in three dimensions in classifying the regular and semi-regular solids. You can see an account of this in this NRICH article by Warwick Evans.

Can you construct some elegant procedures to replicate these images?