1. The document discusses virtual bumblebees, which are modeled after Langton's ants and follow simple rules as they move on a plane, changing the color of squares and turning at each step. 2. Langton's ants move on a grid, turning 90 degrees left at black squares and 90 degrees right at white squares while changing the square's color, and virtual bumblebees similarly turn and change dot colors as they move. 3. These virtual creatures demonstrate self-organized criticality and complex emergent behavior from simple rules, with potential applications including modeling eusocial behavior, network traffic, and screensavers.

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Virtual Bumblebees
James P. Howard, II
MathFest—5 August 2015
Washington, DC

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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.

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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.

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Langton Ant Demonstration

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Steven Levy and Artificial Life
Steven Levy / VintageMarion Ettlinger / Steven Levy

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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.

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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

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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.

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Chase’s Initial Vector

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Beatrix’s Initial Vector

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Bumblebee Explosion

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Langton Ant Simulator

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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