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Stanisław Ulam and the Lwów School of Mathematics
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Program 33 / 47

Notebook 6 · Patterns: the spiral and cellular automata

Steps: draw a spiral by hand

Interactive 8 min

Draw a spiral by hand

You need squared paper and a pencil. This is how Gardner describes the doodle.

  1. Step 1

    Put 1 in the centre

    Choose a square near the middle of the page and write 1 in it.

  2. Step 2

    Write 2 next to it

    Move one square to the right and write 2.

  3. Step 3

    Turn counterclockwise and keep going

    Write 3, 4, 5, … winding outwards. Gardner's account turns counterclockwise.

  4. Step 4

    Circle the primes

    Circle 2, 3, 5, 7, 11, 13 and every other prime you reach.

  5. Step 5

    Look for diagonals

    Do the circles line up? Compare your page with the interactive above.

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