3D Fractals

This program generates and renders a fractal terrain landscape using a midpoint displacement algorithm, converted from an Apple II original to run on the TS-2068. The user specifies a detail level from 1 to 6, which controls the recursion depth; the terrain heights are stored in a 65×33 array `D()` and built up iteratively across X, Y, and diagonal passes. Three rotation subroutines apply horizontal (azimuth) and vertical (elevation) transformations using precomputed sine and cosine values before projecting to screen coordinates. The display loop renders the surface as three sets of isometric line strips using `PLOT`/`DRAW`, with a sea-level clipping routine that interpolates the shoreline crossing point when a line segment transitions between above and below zero height. Scaling factors `XS`, `YS`, and `ZS` are each set to 0.04, and the screen projection applies a fixed perspective correction in the `XP`/`YP` calculation at line 1030.

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Program Analysis

Program Structure

The program is organized into clearly delineated phases: initialization, terrain generation, and display. Control flows from the input and setup block (lines 15–52), through the iterative fractal subdivision loop (lines 60–120), then jumps to the display routines starting at line 640. A final GO TO 1130 at line 750 targets a non-existent line, terminating execution after display — a recognized termination idiom. Line 1150 contains a STOP that is never reached.

Terrain Generation — Midpoint Displacement

The fractal surface is built in a 65×33 array D() (line 20), sized for up to 6 levels: DS = 2^LE + 1, giving a maximum of 65 columns. For each level N (line 60), the roughness scale L = 10000 / 1.8^N decreases geometrically, producing finer detail at each pass. Three subroutines perform the midpoint displacement:

• Lines 150–200: interpolates heights along the X direction.
• Lines 220–270: interpolates heights along the Y direction.
• Lines 290–350: interpolates heights along the diagonal.

Each subroutine computes a new height as the average of two neighbors plus a random offset: (D1+D2)/2 + (RND-0.5)*L/2. The step size SK = IB*2 and interval IB = MX/2^N halve each level, refining the mesh.

Array Access with Symmetry Folding

The read subroutine (lines 370–400) and write subroutine (lines 420–450) apply a symmetry fold when J > MY: the indices are remapped as BY = MX+1-J, BX = MX-I. This exploits the triangular structure of the terrain grid, effectively mirroring the second half of the array rather than storing it separately. Array indices are offset by +1 throughout to avoid the zero-based boundary (D(BX+1, BY+1)).

3D Projection Pipeline

Before plotting, each point passes through a multi-stage transformation pipeline:

1. Sea-level clipping (line 470, subroutine): detects sign changes in ZZ and interpolates the shoreline crossing using parameter W3 = ZZ/(ZZ-Z2).
2. Scaling (line 950): multiplies XX, YY, ZZ by XS=YS=ZS=0.04.
3. Horizontal rotation (lines 770–800): applies azimuth rotation using precomputed RC, RS (cosine/sine of PI/6).
4. Vertical rotation (lines 860–890): applies elevation rotation using VC, VS (cosine/sine of -PI/5).
5. Screen projection (lines 1030–1050): maps to pixel coordinates with XP = XP*0.55+5 and YP = 175-(24-0.7*YP), then draws with PLOT/DRAW.

Sea-Level and Flag Logic

The sea-level subroutine (lines 470–620) tracks whether the current segment is above or below zero height using a flag variable F1. F1=1 (set by line 1070) suppresses drawing; F1=0 (set by line 1090) re-enables it. The sentinel value XO=-999 signals a pen-up state (start of a new strip), analogous to a “move” vs. “draw” distinction. The clipping interpolation correctly handles both transitions: entering water (line 560) and exiting water (line 590).

Display Loops

Three nested loops at lines 660–740 sweep the terrain in three directions to draw isometric wireframe strips:

• Lines 660–680: strips along diagonal slices with J from 0 to I.
• Lines 690–710: strips along rows with I from J to MX.
• Lines 720–740: strips along the diagonal grain using G and H.

Each strip resets XO=-999 at the start to lift the pen. The isometric world coordinates use XX = I/MX*10000 - YY/2 to apply a horizontal shear consistent with a 30° isometric projection.

Notable Anomalies

• The REM comment at line 210 reads “HEIGHTS ALONG X” but actually governs the Y-direction pass (lines 220–270); line 140 correctly labels the X pass.
• Subroutine at line 1110 is an empty stub (just RETURN), presumably a placeholder for screen setup such as clearing or mode switching.
• Lines 760 and 850 each contain a bare REM with no text, used as spacers between subroutines.
• The bounds check at line 1045 (Y8>174 OR Y8<0 OR YP>174 OR YP<0) guards against off-screen PLOT/DRAW calls, preventing errors for extreme height values.