Set the slider to the number of steps in the random walk. Click on the green flag. The particle will pick a random heading (0-360º) and then move 3 steps. The final position of the particle is marked with a violet-colored circle. The Expected Distance is give by L√(n) where L is the average step (3, in this case) and n is the number of steps in the walk. The Expected Distance is marked with a blue-colored circle. The blue circle tells us that a particle that walks n steps is 'expected' to end the walk at any point on the blue circle. Remember, this is a probability expectation therefore the larger the value of n. or the larger the number of trails averaged for a given n, the closer the end point of the actual walk will be to the expected distance. The symbol in the upper left corner represents 'random force'.
This project is the 2-dimensional version of my 1-demsional project, Feynman's Random Walk that can be viewed at http://scratch.mit.edu/projects/11282377/ "In mathematical language, it can be stated that the Brownian motion track is self-similar at all magnifications. This means that if we see a track without any labels on it, we cannot know the magnification at which the track was monitored. The fractal representing Brownian motion has no differential function. Thus Brownian motion satisfies all the theoretical requirements for treating it as a fractal system." A quote from Dr.Brain Kaye. The circles are drawn as defined by my arc-radius script described in my Make a Block project at: http://scratch.mit.edu/projects/10155992/
