Algorithmic #SandMapping

Over the last week, Simone Munao (PhD Mathematics at VU Amsterdam) and Patrick Hafkenscheid (PhD Mathematics candidate at VU Amsterdam) and later also both Bogdan Banu and Gosse Overal that joined spontaneously, worked on some possible algorithms that one could use for #Sandmapping. We picked some proposals to present here.

Achilles

Achilles and the Tortoise

This #SandMapping algorithm is inspired by one of Zeno’s paradoxes: Achilles and the Tortoise.
The rules go as following:

  1. Pick any two objects (for example trees) that you want to connect.
  2. Use a rope to create a straight line between the two objects.
  3. Determine the middle of the rope length use this spot as the center of you first circle
  4. Divide the rope again in two so you know 1/4 of the total length. This is the radius (rope length) which witch you draw the first circle. Draw this circle.
  5. Divide the rope again in two so is has the length 1/8 of the total length
  6. Use the two intersections between the straight line (between the objects) and the first circle as the center point of two new circles.
  7. Continue this way infinite. You will never really reach the trees, but the drawing will clearly show the intention of the draftsman.
meten Drawing
smaller

Circumscribe a Circle on a Triangle

tiangle03

tiangle02The explanation of the construction can be found here

A variation on Achilles and the Tortoise:

Skeching

variation

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