Casio fx-CG 50: Random Walk Histogram
Mosquitos an Inspiration, What?
Inspiration:
Ellenberg, Jordan. Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else Penguin Books: New York, NY. 2021
The beginning of Chapter 4, Sir Ronald Ross proposes the problem: In a simple case, a mosquito can only travel in one of two directions, which is northeast or southwest. The goal was to find the average distance a mosquito is from its home after a given life span.
The program TWALK would address a similar problem.
N = number of trials
S = number of steps the mosquito (or whatever you want to imagine) walks in a single direction
Each trial calculates the final position. The program draws a histogram of all the trails.
TWALK gives two choices:
(-1, 1): Each turn, the mosquito must move forward 1 step or backward 1 step
(-1, 0, 1): Each turn, the mosquito must either move forward 1 step, move backward 1 step, or stay still for one turn.
Drawing an Histogram Program in Casio Programming
Syntax:
S-Grph# DrawOn, Hist, List x, 1, [ColorLinkOff], [Color] ColorLighter
# = Graph 1, 2, 3
List x = List 1 to List 26
Color Commands: ColorLinkOff,
Colors: One of 8 eight colors
ColorLighter: the fill of the color is lighter than the bar
The color commands are optional. If you are using a Casio fx-9750GIII, leave of the color commands.
Casio fx-CG50 Program TWALK
Text:
'ProgramMode:RUN
"EWS 2022-08-04"
"RANDOM WALK 2.0"
"NO. TRIALS"?->N
N->Dim List 26
"NO. STEPS"?->S
Menu "STEPS","_(-)_1,1",2,"-1,0,1",3
Lbl 2:2->F:Goto 1
Lbl 3:3->F:Goto 1
Lbl 1
For 1->I To N
F=2=>Sum (2*RanInt#(0,1,S)-1)->List 26[I]
F=3=>Sum (RanInt#((-)1,1,S))->List 26[I]
Next
"POSITIONS LIST:"Disps
List 26Disps
(-)S->H Start
1->H pitch
S-Gph1 DrawOn,Hist,List 26,1,ColorLinkOff,Blue ColorLighter
DrawStat
On the Screen:
"EWS 2022-08-04"
"RANDOM WALK 2.0"
"NO. TRIALS"?→N
N→Dim List 26
"NO. STEPS"?→S
Menu "STEPS","-1,1",2,"-1,0,1",3
Lbl 2:2→F:Goto 1
Lbl 3:3→F:Goto 1
Lbl 1
For 1->I To N
F=2⇒Sum (2×RanInt#(0,1,S)-1)→List 26[I]
F=3⇒Sum (RanInt#(-1,1,S))→List 26[I]
Next
"POSITIONS LIST:"◢
List 26◢
-S->H Start
1->H pitch
S-Gph1 DrawOn,Hist,List 26,1,ColorLinkOff,Blue ColorLighter
DrawStat
Examples
N = 50, S = 5
(-1, 1): Mosquito cannot rest
.jpg)
(-1, 0, 1): Mosquito can rest
.jpg)
Wishing you an excellent day,
Eddie
All original content copyright, © 2011-2022. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
