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1
Virtual Bumblebees
James P. Howard, II
MathFest—5 August 2015
Washington, DC
2
Artificial life uses information concepts and computer modeling to
study life in general, and terrestrial life in particular. It aims to explain
particular vital phenomena, ranging from the origin of biochemical
metabolisms to the coevolution of behavioral strategies, and also the
abstract properties of life as such (“life as it could be”).
Artificial Life
The MIT Encyclopedia of the Cognitive Sciences, (Cambridge, Mass: MIT Press, 1999), 37.
3
Squares on a plane are colored variously either black or white. We
arbitrarily identify one square as the "ant". The ant can travel in any of
the four cardinal directions at each step it takes. The ant moves
according to the rules below:
• At a white square, turn 9oº right, flip the color of the square, move
forward one unit
• At a black square, turn 90º left, flip the color of the square, move
forward one unit
The Virtual Ant’s Rules
Langton's ant. (n.d.). In Wikipedia. Retrieved July 22, 2015, from https://en.wikipedia.org/wiki/Langton%27s_ant.
4
Langton Ant Demonstration
5
Steven Levy and Artificial Life
Steven Levy / VintageMarion Ettlinger / Steven Levy
6
The vant itself was a V-shaped construct that moved in the direction of
its point. If the lead cell moved into a blank square on the imaginary
grid, the vant continued moving in that direction. If the square was
blue, the vant turned right and changed the color of that cell to yellow.
If the square was yellow, the vant turned left and changed the color of
the square to blue.
Levy's Description
Steven Levy, Artificial Life: A Report from the Frontier Where Computers Meet Biology, Pantheon Books, 1992, 104.
7
1. At a red dot, turn 90 degrees to the right, turn the dot blue, and
move forward one cell;
2. At a blue dot, turn 90 degrees to left, turn the dot red, and move
forward one cell; and
3. At an empty square, move forward one cell.
Bumblebee Rules
8
Vants reside in an environment that consists of uniformly spaced, fixed
cells that are in one of two states (either blue or yellow in the following
figures). A vant travels in a straight line in empty space. If it
encounters a blue cell, it turns fight and leaves the cell colored yellow.
If it encounters a yellow cell, it turns left and leaves the cell colored
blue.
The Langton Ant
Christopher G. Langton, “Studying artificial life with cellular automata.” Physica D: Nonlinear Phenomena, 22(1), 120-149.
9
Chase’s Initial Vector
10
Beatrix’s Initial Vector
11
Bumblebee Explosion
12
Langton Ant Simulator
13
Applications
• Eusocial behavior
• Network traffic
• Awful screensavers
Next Steps
• Extend to 3, 4, or n dimensions
• Determine if the bees are
turmites
What’s Next

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Virtual Bumblebees

  • 1. 1 Virtual Bumblebees James P. Howard, II MathFest—5 August 2015 Washington, DC
  • 2. 2 Artificial life uses information concepts and computer modeling to study life in general, and terrestrial life in particular. It aims to explain particular vital phenomena, ranging from the origin of biochemical metabolisms to the coevolution of behavioral strategies, and also the abstract properties of life as such (“life as it could be”). Artificial Life The MIT Encyclopedia of the Cognitive Sciences, (Cambridge, Mass: MIT Press, 1999), 37.
  • 3. 3 Squares on a plane are colored variously either black or white. We arbitrarily identify one square as the "ant". The ant can travel in any of the four cardinal directions at each step it takes. The ant moves according to the rules below: • At a white square, turn 9oº right, flip the color of the square, move forward one unit • At a black square, turn 90º left, flip the color of the square, move forward one unit The Virtual Ant’s Rules Langton's ant. (n.d.). In Wikipedia. Retrieved July 22, 2015, from https://en.wikipedia.org/wiki/Langton%27s_ant.
  • 5. 5 Steven Levy and Artificial Life Steven Levy / VintageMarion Ettlinger / Steven Levy
  • 6. 6 The vant itself was a V-shaped construct that moved in the direction of its point. If the lead cell moved into a blank square on the imaginary grid, the vant continued moving in that direction. If the square was blue, the vant turned right and changed the color of that cell to yellow. If the square was yellow, the vant turned left and changed the color of the square to blue. Levy's Description Steven Levy, Artificial Life: A Report from the Frontier Where Computers Meet Biology, Pantheon Books, 1992, 104.
  • 7. 7 1. At a red dot, turn 90 degrees to the right, turn the dot blue, and move forward one cell; 2. At a blue dot, turn 90 degrees to left, turn the dot red, and move forward one cell; and 3. At an empty square, move forward one cell. Bumblebee Rules
  • 8. 8 Vants reside in an environment that consists of uniformly spaced, fixed cells that are in one of two states (either blue or yellow in the following figures). A vant travels in a straight line in empty space. If it encounters a blue cell, it turns fight and leaves the cell colored yellow. If it encounters a yellow cell, it turns left and leaves the cell colored blue. The Langton Ant Christopher G. Langton, “Studying artificial life with cellular automata.” Physica D: Nonlinear Phenomena, 22(1), 120-149.
  • 13. 13 Applications • Eusocial behavior • Network traffic • Awful screensavers Next Steps • Extend to 3, 4, or n dimensions • Determine if the bees are turmites What’s Next

Editor's Notes

  1. Artificial life has been used to model natural phenomenon The most well-known example is probably Conway's Life Also well known is the flocking dinosaur movements in the original Jurassic Park
  2. Created in 1986 by Christopher Langton The rules provide for an orthogonal field Ants cannot be "born" through the rules, only move
  3. This is recorded from Ross Scrivener's website I clicked in a few locations without planning Just wanted to get a sample and flavor of the ant's behavior
  4. Book was published in the summer of 1993 Found a copy at the Lane Public Library I had a new toy
  5. Levy's description is very different from the explanation on Wikipedia The description includes three different cell states Different from every implementation of the vants I had seen
  6. I started with Scrivener's implementation, one day Reimplemented the Levy version. I turned them yellow and called them bumblebees, instead These are rules, distilled
  7. Going back to the literature This is the original explanation from Physica D This is what Levy described Now I have a mystery
  8. This is Chase's initial vector Chase is my five year old He thinks this is a video game
  9. Beatrix's vector is also cool She is 3 She was upset my laptop did not have a touchscreen
  10. This shows a local favorite, the bumblebee explosion The system is implemented such that a bee has a location on the field Multiple bees can occupy the same location The cells will flip as each bee is processed The bees travel together until they disperse to their own path's
  11. This reimplements the "traditional" virtual ant Demonstrates the bees are a turning machine