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Download the 7 sprites and 9 scripts of "The Random Walk" and open it in Scratch Project Notes
We imagine a "game" in which a player - cat starts at the point x=0 and at each move is required to take a step either forward (towards +x) or backward (towards -x). The choice is to be made randomly, determined by the toss of a coin. How far does he get on the average?
The step equals 3 (thanks mathjp)
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My maximum walk was 96.
Today, the maximum walk was 150!
I established in theory that the average number of returns originally during 2n stages is approximately 2*sqr(n / pi) -1 for example for 10 jumps n=5 the average number on returning to the origin is 1.52 . For 100 jumps ( n=50 ) it is 6.97 for 1000 jumps 43.58. If the probability is not 1/2 for right (example 0.6) there are a new problem. Scratch is a infinite generator of problemes for me !
(view all replies)Simulations of these random walks lead to very long walks! We can show in theory that the average of the durations of these walks does not stabilize around a fixed point. If we have exactly a proba of 1/2 the particle returns in theory originally with a probability of 1 but the average number of stages to reach this objective is infinite!
(view all replies)A theorical reference is :http://en.wikipedia.org/wiki/Random_walk
(view all replies)Fascinating! The random cat can get quite far, it seems. It would be interesting to try a different look and see how long it takes for the cat to return to the zero point. It would be a different project though...not how far the cat walks but how long the walk takes :)
Thanks for your suggestions. I wanted to do a project based on the proposition of Feynman (book, "The Feynman Lectures on Physics", ed. 1966).
Very good idea. It's the problem ! It's possible to make simulation or...(for Jens : STOCHASTIK von Arthur Engel. Ernst Klett Verlag Stuttart: Klett 1987)(Markov chain wikipedia))
(view all replies)Whoa what a super intelligent project. Thanks, Regards, Ahaan
I think this game can show why I never win in EuroMillions: in 10 balls, only 2 fell in the positive area, with 12 and 78. The others fell between -138 and -18. The luck is bad but the game is good
Cool project for random walk. I don't know if it is a coincidence 60,90,12,24,12,180,54,42,24,54 my answers are divisible by 6 too. Largest:180
This is a project close related to Brownian motion. Your project remind me the approch of Feynman. Thanks!
No it's not a coincidence nevit. It's because x=3 and the total number of move 's an even number!
(view all replies)Very good project. Il faut préciser que x=3. En français cet exercice a pour nom "la marche de l'ivrogne" l'origine O étant un réverbère !
it is similar to lightning.
Thanks, it is very interesting! I love it! I notice all answers are divisible by 6.
It's because x=3 and the total number of move 's an even number!
(view all replies)