TI-84 Plus CE: Logistic Map
It feels like forever since I with the TI-84 Plus CE.
Introduction
The program LOGISTIC plots the sequence
x = r * x * (1 – x)
where x is initially in the interval (0, 1) and r is a parameter. The sequence traces out the path of recursion.
Depending on the value of r, the sequence can eventually stabilize to a single point, fluctuate then stabilize, eventually bounce between two stable points, or going into the chaos. The higher the r, chance of the latter two possibilities increase. Typically, for any r < 3, the sequence will most likely stabilize.
TI-84 Plus CE Program: LOGISTIC.8xp
Type: TI-Basic Program
ClrHome
Disp “LOGISTIC MAP”
Disp “X1=R*X0*(1-X0)”
Seq
FnOff
Menu(“LAMBDA (R)”, “ENTER”, 1, “RANDOM”, 2)
Lbl 1
Input “0<R≤4: “, R
Goto A
Lbl 2
randInt(1,80) / 20 → R
Pause R
Goto A
Lbl A
Menu(“U(1)=”, ”ENTER”, 3, “RANDOM”, 4)
Lbl 3
Input “U(1)? “, U
Goto B
Lbl 4
rand → U
Pause U
Goto B
Lbl B
{U} → u(nMin)
SEQ(n+1)
“R*u(n)*(1-u(n))” → u
FnOn 1
1 → nMin
50 → nMax
0 → Ymin
1 → Ymax
0 → Xmin
50 → Xmax
DispGraph
Notes:
The Time setting is assumed: x-axis = n, y-axis = u__n
nMin: Sets the counter and the index of the first argument. Typically the counter starts with 0 or 1. Keystrokes: [ vars ], 1. Window, scroll to U/V/W, 4. nMin.
Seq: Sets Sequence mode.
I use R for λ since the TI-84 does not have Greek characters (except for π and σ).
randInt(1,80) / 20 → R: Selects random values from 0.05 and 4 with a tick mark of 0.05.
u(nMin): Store the initial conditions. The conditions are entered as a list, even there is only one initial condition. Keystrokes: [ vars ], 1. Window, scroll to U/V/W, 1. u(nMin)
SEQ(n+1): In the program editor, I had to select this from the catalog. It is listed under “SEQ(n+1) Type”. This allows for the recurring sequence to be in the format u(n+1) = f(u(n),n).
“R*u(n)*(1-u(n))” → u: The u is type from the keyboard: [ 2nd ] [ 7 ].
FnOn 1: Turns the sequence u(n) on.
Examples
Left: r = 3.67, initial point = 0.2. This looks like total chaos as n grows.
Right: r = 3.1, initial point = 0.5. This sequence does not converge to a single value, but eventually provides a bifurcation between two points.
Caution: If r is too high, even if the u(1) is with in the interval [0, 1], the sequence can “escape” and an overflow can occur. I don’t recommend an r higher than 4.
Source
“Logistic map”. Wikipedia https://en.wikipedia.org/wiki/Logistic_map Retrieved October 20, 2025.
Eddie
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