I am new to graphic calculators and am working my way through the TI-83 plus manual. I got to the Sierpinski triangle example on page 17-7. It worked as expected but I thought I would investigate what is happening with some of the calculations. Instead of a random numbers for X, Y, and N, I put in a starting value of 1 for X and Y and a constant of 0.2 for N. I also shortened the loop to only a dozen of iterations or so. With the N less than 1/3, the X and Y values should be halved for each iteration. This is true for X, but Y goes to zero after the first go around. This makes no sense to me. I tried a bunch of different changes to see why. Curiously, when I use another variable letter throughout the program rather than Y, it works just as expected showing a halved value for both X and the second variable.

While the program works as presented in the text with random numbers, I sure would like to know what is happening when one uses the variable Y so I can be confident in my results for future programming applications. There must be something I am missing. Thanks in advance for any insight. Code is below for both the original and modified program.

ORIGINAL PROGRAM

MODIFIED PROGRAM

While the program works as presented in the text with random numbers, I sure would like to know what is happening when one uses the variable Y so I can be confident in my results for future programming applications. There must be something I am missing. Thanks in advance for any insight. Code is below for both the original and modified program.

ORIGINAL PROGRAM

**Code:**```
PROGRAM:SIERPINS
```

:FnOff :ClrDraw

:PlotsOff

:AxesOff

:0→Xmin:1→Xmax

:0→Ymin:1→Ymax

:rand→X:rand→Y

:For(K,1,3000)

:rand→N

:If N≤1/3

:Then

:0.5(0.5+X)→X

:0.5(0.5+Y)→Y

:End

:If 1/3<N and N≤2/3

:Then

:0.5(0.5+X)→X

:0.5(1+Y)→Y

:End

:If 2/3<N

:Then

:0.5(1+X)→X

:0.5Y→Y

:End

Pt-On(X,Y)

:End

:StorePic 6

MODIFIED PROGRAM

**Code:**```
PROGRAM:SIERPINS
```

:FnOff :ClrDraw

:PlotsOff

:AxesOff

:0→Xmin:1→Xmax

:0→Ymin:1→Ymax

:1→X:1→Y

:For(K,1,12)

:.2→N

:If N≤1/3

:Then

:0.5(0.5+X)→X

:0.5(0.5+Y)→Y

:End

:If 1/3<N and N≤2/3

:Then

:0.5(0.5+X)→X

:0.5(1+Y)→Y

:End

:If 2/3<N

:Then

:0.5(1+X)→X

:0.5Y→Y

:End

Pt-On(X,Y)

:End

:StorePic 6