## Saturday, October 1, 2022

### Casio fx-CG 50: Random Walk Histogram

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

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

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

DrawStat

On the Screen:

"EWS 2022-08-04"

"RANDOM WALK 2.0"

"NO. TRIALS"?→N

N→Dim List 26

"NO. STEPS"?→S

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

DrawStat

Examples

N = 50, S = 5

(-1, 1):  Mosquito cannot rest

(-1, 0, 1): Mosquito can rest

Wishing you an excellent day,

Eddie

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