... as always, it took a bit of trial & error, and Copilot didn't get it right until I supplied the following hint: 

Hence, previous attempts looked like this:

;
; Largely written by Copilot, with some help by Michael Wessel
; 2/12/2026 (i.e., to get the display "shearing" right - it was stuck there)
;

; =========================================================
; Firmware ROM Routines (ET‑3400 Monitor)
; =========================================================

RESET       = $FC00
INCH        = $FDF4
ENCODE      = $FDBB
OUTCH       = $FE3A
OUTHEX      = $FE28
OUTBYT      = $FE20
OUTST1      = $FE50
OUTST0      = $FD8D
DSPLAY      = $FD7B
REDIS       = $FCBC


; =========================================================
; ET‑3400 + 128×32 OLED
; Sierpinski fractal using logical coordinates (LX, LY)
; Display shear applied only during plotting:
;
;     ScreenX = LX + (LY >> 1)
;     ScreenY = LY
;
; This preserves the pure Sierpinski logic (LX & LY == 0)
; while visually tilting the triangle on the OLED.
;
; Variables at $0100, code at $1000
; =========================================================

            ORG   $0100

; -----------------------------
; Logical fractal coordinates
; -----------------------------
LX:         RMB   1      ; logical X coordinate
LY:         RMB   1      ; logical Y coordinate

; -----------------------------
; Screen coordinates (after shear)
; -----------------------------
SX:         RMB   1      ; screen X = LX + (LY >> 1)
SY:         RMB   1      ; screen Y = LY

COL:        RMB   1      ; pixel color (0xFF = on)


; -----------------------------
; Temporary scratch
; -----------------------------
T1:         RMB   1      ; holds LY >> 1


; =========================================================
; CODE SECTION
; =========================================================
            ORG   $1000


; ---------------------------------------------------------
; MAIN — Sierpinski in logical space, sheared only in plotting
; ---------------------------------------------------------
MAIN:
            JSR   CLEARSCREEN
            JSR   INCH

            CLR   LY          ; start at logical Y = 0

Y_LOOP:
            CLR   LX          ; start each row at logical X = 0

X_LOOP:
; ---------------------------------------------------------
; Sierpinski test in logical space:
;     (LX & LY) == 0  → pixel is part of the fractal
; ---------------------------------------------------------
            LDAA  LX
            ANDA  LY
            BNE   SKIP_PLOT   ; if nonzero → skip pixel

; ---------------------------------------------------------
; Compute screen coordinates:
;
;   SX = LX + (LY >> 1)
;   SY = LY
;
; This applies a gentle shear to the right, visually
; turning the square-grid Sierpinski into a triangular one.
; ---------------------------------------------------------
            LDAA  LY
            LSRA               ; LY >> 1
            STAA  T1           ; T1 = LY/2

            LDAA  LX
            ADDA  T1           ; SX = LX + (LY/2)
            STAA  SX

            LDAA  LY
            STAA  SY           ; SY = LY

; ---------------------------------------------------------
; Plot pixel at (SX, SY)
; ---------------------------------------------------------
            LDAA  #$FF
            STAA  COL
            JSR   PLOTNU       ; your non-updating plot routine

SKIP_PLOT:
; ---------------------------------------------------------
; Advance logical X
; ---------------------------------------------------------
            INC   LX
            LDAA  LX
            CMPA  #128
            BCS   X_LOOP       ; continue while LX < 128

; ---------------------------------------------------------
; Advance logical Y
; ---------------------------------------------------------
            INC   LY
            LDAA  LY
            CMPA  #32
            BCS   CONT         ; continue while LY < 32

; ---------------------------------------------------------
; Finished — start over after keypress
; ---------------------------------------------------------
DONE:
            JSR INCH
	    JSR MAIN

; ---------------------------------------------------------
; End-of-row housekeeping
; ---------------------------------------------------------
CONT:
            JSR   PLOT         ; your update/refresh routine
            BCS   Y_LOOP       ; branch always (BCS always true after JSR)


; ---------------------------------------------------------
; CLEARSCREEN
; ---------------------------------------------------------
CLEARSCREEN:
        PSHA
        LDAA  #$00
        JSR   EXEC
        PULA
        
        JSR LDELAY
        JSR LDELAY 
        
        RTS


; ---------------------------------------------------------
; PLOTNU — high-level plot using EXEC, NO UPDATE
; ---------------------------------------------------------
PLOTNU:
        LDAA  #$0A
        JSR   EXEC

        LDAA  sx
        JSR   EXEC

        LDAA  sy
        JSR   EXEC

        LDAA  col
        JSR   EXEC

        JSR   DELAY
        RTS


; ---------------------------------------------------------
; PLOT — high-level plot using EXEC, WITH SCREEN UPDATE
; ---------------------------------------------------------
PLOT:
        LDAA  #$0B
        JSR   EXEC

        LDAA  sx
        JSR   EXEC

        LDAA  sy
        JSR   EXEC

        LDAA  col
        JSR   EXEC

        JSR   LDELAY
        RTS


; ---------------------------------------------------------
; PLOT0 — disp pixel output
; ---------------------------------------------------------
PLOT0:
        JSR   REDIS

        LDAA  sx
        JSR   OUTBYT

        LDAA  sy
        JSR   OUTBYT

        LDAA  col
        JSR   OUTBYT

        RTS


; ---------------------------------------------------------
; EXEC — write A to $1800 with timing
; ---------------------------------------------------------
EXEC:
        NOP
        NOP
        NOP
        NOP
        NOP
        NOP
        NOP

        STAA  $1800

        NOP
        NOP
        NOP
        NOP
        NOP
        NOP
        NOP

        NOP
        NOP
        NOP
        NOP
        NOP
        NOP
        NOP
        JSR   DELAY

        RTS


; ---------------------------------------------------------
; DELAY — coarse delay
; ---------------------------------------------------------
DELAY:
        PSHA
        PSHB

        LDAA  #$01
OUTER:  LDAB  #$FF

INNER:  DECB
        BNE   INNER

        DECA
        BNE   OUTER

        PULB
        PULA
        RTS


; ---------------------------------------------------------
; LDELAY — longer delay
; ---------------------------------------------------------
LDELAY:
        PSHA
        PSHB

        LDAA  #$05
LOUTER: LDAB  #$FF

LINNER: DECB
        BNE   LINNER

        DECA
        BNE   LOUTER

        PULB
        PULA
        RTS