Straight from me!

In Geometry on Friday we watched the following documentary on fractals. Now a fractal is a geometric pattern that is repeated at every scale and so cannot be represented by classical geometry. It also repeats itself under several levels of magnification,and as a result is a shape that appears irregular at all scales of length.

After watching the documentary (which was made before I was born) I decided to try to create a fractal generator of my own!

First off I tried creating a simple generator of the equations numbers using the ti-84 keypad for my ti-nspire.

Now first off I was trying to do the fractal called the M-Set which has an equation of :

Z⇔Z^2+C

As a result I started programing for the ti 84 with the following code:


ClrHome
Prompt C
Prompt Z
CtrHome
While 1=1
Z^2+C→A
Disp A
A^2+C→Z
Disp Z
Pause
End


So What happens is 1. everything on the screen is cleared (a pet peeve of mine to have a clean screen at start of a program), then it asks what number you want for C and then which one for Z. It then clears the screen once again and then since 1=1 will never be false the program should keep running Z^2+C then displaying the answer, then solving A^2+C and then displaying that answer and repeating for ever it every time they presses the enter button. The program though produces the an overflow error because its number can not fill the screen. As a result I just modified it to stop every time the numbers get too big for the calculator:


ClrHome
Prompt C
Prompt Z
CtrHome
1e^(70)→Q
1→R
While R Z^2+C→A
Disp A
A^2+C→Z
Z→R
Disp Z
Pause
End


In the modified code the program this time runs until the numbers calculated are too big for the calculator.

Here is a sample output of my program

C=1

Z=2

5

26

677

458330

2.100663888e11

4.412788775e22

1.947270477e45

3.79186231e90

Done

As of right now I am still working on a script to graph a fractal but I am working on it right now. I am also working on a php script which will produce a fractal in an image on the fly (that one is almost done just some testing left).

(Please note my calculator has the following settings under mode as different settings my get you different answers:

Normal

Float

Degree

Func

Connected

Sequential

Real

Full

)