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Beginners to LOGO programming may want to start by working through the FIRST FORWARD series of introductory articles before tackling this problem.
As is often the case when looking for something, you become distracted by other more exciting ideas. Such was the case recently when retrieving some old tiling patterns.
How could I have overlooked the Penrose tile? A very special tile named after its inventor - Sir Roger Penrose OM, until recently the Rouse Ball Professor of Mathematics at the University of Oxford. He is also a well-known populariser of mathematics.
The Penrose tile is a rhombus whose side length is $\phi$ (phi - the Golden section) and whose interior angle is $72^\circ$.
The tile is cleverly dissected into what John Conway - another well-known populariser of mathematics,
These two shapes can be used to tile the plane in very interesting and stimulating ways, as illustrated below:
Can you, by first defining the kite and dart within the context of LOGO, devise elegant programs to replicate the tilings above?
There is an article about these tilings by Bill Richardson in the January 2000 edition of Maths in School, published by the Mathematical Association. Bill has sent us this image showing much more of the second tiling pattern above. You might like to try to re-produce it using LOGO. |