So Angry that I made this before the competition:

Code:

:"Best used with inverted colors
:"0000300330030000000003033030000000000033330000000003300330033000300333033033300303003333333300300030033333300300333333333333333333333333333333330030033333300300030033333333003030033303303330030003300330033000000000333300000000000303303000000000300330030000"
ClrHome
DelVar L₁
1→L₁(1):3→L₁(2):7→L₁(3):12→L₁(4):18→L₁(5):23→L₁(6):1→L₁(7):3→L₁(8):7→L₁(9):9→L₁(10):10→L₁(11):5→L₁(12)
While getKey≠105
Output(10,1,"XXXIXXXXXIXXXXXIXXXXXIXXXX
Output(9,1,"IEEEEEIEEEEEIEEEEEIEEEEEIE
Output(8,1,"XX I XXX I XXX I XXX I XXX
Output(7,1,"I EEE I EEE I EEE I EEE I
Output(6,1,"X  I  X  I  X  I  X  I  X
Output(5,1,"   E     E     E     E   
For(M,1,4
Output(M,1,"                         
End
For(M,1,6
Output(L₁(M+6),L₁(M),"*
(randInt(­1,1)+L₁(M))→A
If A≤0:26→A
If A≥27:1→A
A→L₁(M)
End
For(M,7,12
(L₁(M)+1)→A:If A=11:1→A
A→L₁(M)
End
End

Idea for the screensaver:
TI-Basic
every 20 cycles or so change the screensaver
use the home screen
come up with gentile looking but unique screen savers
have it within one Repeat loop of Getkey to make it easily escapable

(ideas so far):
Center screen ripple
night sky with twinkling stars
Got 3 simple TI-Basic Screen savers made, need to make some home screen screensavers because the graph does not save the entire screen. Need to look up the Asm( routine for color inversion (likely not happening as this has the potential to force me to fight over the spot with the non-ti basic players and get filleted by their better coding skills, creativity and control over the calculator).

Code:
:DCS
"0000000330000000000000033000000000000003300000000000000330000000000033333333000000003333333300000000333333330000333333333333333333333333333333330000333333330000000033333333000000003333333300000000000330000000000000033000000000000003300000000000000330000000"
While getKey≠105
0→Xmin
0→Ymin
100→Xmax
100→Ymax
3→B
BackgroundOff
ClrDraw
randInt(1,5)→A
If A=1
Then
For(A,1,50
randInt(0,100)→L₁(A)
randInt(0,100)→L₂(A)
End
ClrDraw
For(C,1,50
For(A,1,25
Pt-On(L₁(A),L₁(A+25),(1(B=3)+3(B=1)),WHITE
Pt-On(L₁(A),L₁(A+25),B,BLACK
Pt-On(L₂(A),L₂(A+25),(1(B=3)+4(B=1)),WHITE
Pt-On(L₂(A),L₂(A+25),(4(B=3)+1(B=1)),MEDGRAY
1(B=3)+3(B=1)→B
End
End
End
randInt(1,5)→A
If A=1
Then
ClrDraw
For(A,1,10)
randInt(0,100)→L₁(A)
End
For(A,1,10
0→L₁(10+A)
End
11→B
For(A,1,100
For(E,1,5
Pt-On(L₁(E),L₁(E+5),2,B
For(F,0,1
randInt(­1+(int(L₁(5F+10+E)/2)),1+(int(L₁(5F+10+E)/2))→C
C+L₁(E+10+5F)+L₁(E+5F)→L₁(E+5F)
If L₁(E+5F)>100:0→L₁(E+5F):If L₁(E+5F)<0:100→L₁(E+5F)
C→L₁(E+10+F)
End
13(B=11)+12(B=13)+15(B=12)+19(B=15)+11(B=19)→B
End
End
End
randInt(1,5)→A
If A=1
Then
randInt(11,25)→L₁(1)
100→L₁(2):100→L₁(3):0→L₁(4):0→L₁(5)
For(C,1,20
For(A,int(L₁(4)),int(L₁(2)),.5
Line(A,L₁(5),A,L₁(3),L₁(1)
End
randInt(int(L₁(4)),int(L₁(2)/2(C≤5))→L₁(4)
int(L₁(4))→L₁(4
L₁(4)+int(L₁(2)/2)→L₁(2)
int(L₁(2))→L₁(2)
randInt(int(L₁(5)),int(L₁(3)/2(C≤5)→L₁(5)
int(L₁(5))→L₁(5)
L₁(5)+int(L₁(3)/2)→L₁(3)
int(L₁(3))→L₁(3)
randInt(11,21)→L₁(1)
End
End
End

This contains so far:
Left bias snakes
Twinkling stars
generic rectangle formation

New Ideas:
The classic DVD screen saver but "TI84+CE" instead
ripples
impressive. I tried it out in cemu and for being purely in ti basic, its pretty good
  
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