--- title: "IBM" id: 71080 type: "computer_media" slug: "ibm" url: "http://localhost/computer_media/ibm/" markdown_url: "http://localhost/computer_media/ibm.md" published_at: "2026-08-27T20:55:25+00:00" modified_at: "2026-08-27T20:56:35+00:00" author: "David Anderson" featured_image: url: "http://localhost/wp-content/uploads/2026/08/ibm.png" alt: "IBM screen" excerpt: "Three mesmerizing geometric figures unfold through iterative corner-cutting, each grid of spiraling polygons replaced by the next in an endless loop." category: - name: "Archived Media" slug: "archived-media" taxonomy: "category" url: "http://localhost/category/archived-media/" post_tag: - name: "Downloadable" slug: "downloadable" taxonomy: "post_tag" url: "http://localhost/tag/downloadable/" - name: "TS 2068" slug: "ts2068" taxonomy: "post_tag" url: "http://localhost/tag/ts2068/" model: - name: "Timex/Sinclair 2068" slug: "ts-2068" taxonomy: "model" url: "http://localhost/model/ts-2068/" indiv: - name: "Ted Knyszek" slug: "ted-knyszek" taxonomy: "indiv" url: "http://localhost/indiv/ted-knyszek/" genre: - name: "Demo" slug: "demo" taxonomy: "genre" url: "http://localhost/type/demo/" - name: "Graphics" slug: "graphics" taxonomy: "genre" url: "http://localhost/type/graphics/" media_type: "Program" programmers: - name: "Ted Knyszek" slug: "ted-knyszek" taxonomy: "indiv" url: "http://localhost/indiv/ted-knyszek/" download_url: "https://archive.org/download/timex-sinclair-software-archive/IBM%20%28198x%29%28Knyszek%2C%20Ted%29%28TS2068%29%28US%29%28Program%29.zip" mediadate: "198x" images: - url: "http://localhost/wp-content/uploads/2026/08/ibm.png" alt: "IBM screen" media_type_tags: "Demo, Graphics" --- # IBM This program draws three successive animated fractal-like geometric figures using an iterative corner-cutting (Chaikin-style) algorithm, then loops continuously. Each section initializes a set of control points and repeatedly replaces them with weighted interpolations between adjacent vertices — parameterized by `SU` (step ratio) and `RU = 1 – SU` — drawing the evolving polygon at each iteration with PLOT and DRAW. The first section renders a 4×4 grid of quadrilateral spirals with alternating vertex orientations; the second draws a triangular grid pattern with sign-flipped coordinates to create a diamond-like arrangement; the third generates a hexagonal grid. Between each section, `RANDOMIZE USR 50450` is called (likely a ROM routine or machine code entry point for a screen effect), followed by a PAUSE and CLS before the next figure begins. *** ### Program Structure The program is divided into four logical blocks, separated by `PAUSE`, `CLS`, and a final `GO TO 1` that creates an infinite loop: 1. **Lines 1–120:** Setup and first figure — a 4×4 grid of quadrilateral (4-point) iterative spirals. 2. **Lines 210–330:** Second figure — a triangular (3-point) grid arranged in a diamond/chevron pattern with sign-alternating offsets. 3. **Lines 410–530:** Third figure — a hexagonal (6-point) grid drawn across a 3×3 arrangement. 4. **Line 540:**`GO TO 1` restarts the entire sequence. Each section shares the same core algorithmic pattern: initialize control points into arrays `X()` and `Y()`, then iterate a corner-cutting loop that draws the current polygon and updates the vertices. ### Corner-Cutting Algorithm The geometric engine is a variant of the Chaikin corner-cutting algorithm. At each iteration, every vertex `M` is replaced by a weighted average of itself and the next vertex `NJ`: - `T(M) = RU * X(M) + SU * X(NJ)` - `K(M) = RU * Y(M) + SU * Y(NJ)` The ratio `SU` controls how aggressively the corners are cut. Values used are `0.12` (section 1), `0.1` (section 2), and `0.2` (section 3). After each iteration the polygon is drawn before the points are updated, producing a visual spiral as the shape converges inward toward a smooth curve. Wrap-around indexing for the “next vertex” uses the modulo idiom: `NJ = INT(M - N * INT(M/N)) + 1`, where N is the number of vertices (4, 3, or 6 depending on section). This avoids an explicit `IF` branch for the wrap. ### Section 1 — Quadrilateral Grid (Lines 10–120) A 4×4 grid is formed by double-nested `FOR I=0 TO 3 / FOR J=0 TO 3` loops. The parity of `I` and `J` (computed via `INT(I - 2*INT(I/2))`, i.e., `I MOD 2`) determines which of two Y-coordinate configurations is used, creating alternating orientations that tile the screen. Each cell draws 19 iterations (`N=0 TO 18`) of the 4-point spiral. ### Section 2 — Triangular Grid (Lines 210–310) This section is the most complex. It uses variables `II` and `JJ` (toggling between −1 and 1) to alternate the vertical direction of each triangle, producing a diamond/chevron tiling. A guard condition `IF I4-J THEN GO TO 310` skips cells outside a triangular region of the 5×4 grid, giving an overall diamond outline. The color index `C` cycles through values 1–3 (using modulo-3 arithmetic) to change the ink color of successive triangles, though the `PLOT`/`DRAW` calls do not explicitly set INK attributes here — `C` is computed but not visibly applied via `INK C`, making this a likely artifact of the IBM-to-TS-2068 conversion. ### Section 3 — Hexagonal Grid (Lines 410–510) Six control points define a regular hexagon, and an offset `E` (0 or 31) is applied when `I=1` to vertically stagger the middle column, producing a honeycomb-like offset grid. The loop iterates 21 times (`N=0 TO 20`) per cell. Coordinate scaling by factors of `0.8` (X) and `0.9` (Y) maps the hexagons to the screen dimensions with a slight horizontal compression. A guard `IF J=0 AND I<>1 THEN GO TO 510` suppresses cells in the first row except the center, shaping the overall pattern. ### Machine Code Call Each section ends with `RANDOMIZE USR 50450`. Address 50450 is outside the normal BASIC area and points to machine code — likely a screen transition or flash effect injected into RAM or the system area. The use of `RANDOMIZE USR` rather than a BASIC subroutine call indicates a deliberate low-level hook, possibly producing an animated wipe or color fill between figures. ### Key BASIC Idioms - **Modulo via INT:**`INT(X - N * INT(X/N))` used throughout for wrap-around indexing and parity checks, since the ZX BASIC dialect lacks a `MOD` operator. - **Double-buffered arrays:** Temporary arrays `T()` and `K()` hold updated vertex positions while the originals are still being read, then copied back — essential for correct simultaneous update. - **Single-pass draw:** The innermost loop draws the polygon edge before updating points, so each of the N iterations renders a visible polygon, creating the spiral effect with no separate display step needed. ### Potential Anomalies - In section 2, the variable `C` is incremented and modulo-cycled but never used in an `INK` or `PAPER` statement. This strongly suggests the original IBM program used color commands that were not fully translated in the conversion. - The `DRAW` in line 280 uses `(X2-X1)` and `((Y2-30)-(Y1-30))` — the subtraction of 30 from both Y values cancels out, making this equivalent to `(Y2-Y1)`. This is a harmless redundancy, likely a transcription artifact. - Array dimensions `DIM X(6)` etc. at line 10 allocate 6 elements, sufficient for all three sections (max 6 vertices in section 3), so no out-of-bounds access occurs even in sections using fewer vertices. ## Source Code ``` 1 BORDER 0:PAPER 0:INK 7:CLS 5 REM CONVERTED FROM IBM TO TS-2068 BY TED KNYSZEK 10 DIM X(6):DIM Y(6):DIM T(6):DIM K(6) 20 LET SU=.12:LET RU=1-SU 30 FOR I=0 TO 3:FOR J=0 TO 3:IF INT (I-2* INT (I/2))= INT (J-2* INT (J/2)) THEN GO TO 50 40 LET Y(1)=43:LET Y(2)=0:LET Y(3)=0:LET Y(4)=43:GO TO 60 50 LET Y(1)=0:LET Y(2)=43:LET Y(3)=43:LET Y(4)=0 60 LET X(1)=1:LET X(2)=1:LET X(3)=64:LET X(4)=64 70 FOR N=0 TO 18:LET X1=X(4)+I*63:LET Y1=Y(4)+J*43 80 FOR M=1 TO 4:LET X2=X(M)+I*63:LET Y2=Y(M)+J*43 90 PLOT X1,Y1:DRAW (X2-X1),(Y2-Y1):LET X1=X2:LET Y1=Y2:LET NJ= INT (M-4* INT (M/4))+1 100 LET T(M)=RU*X(M)+SU*X(NJ):LET K(M)=RU*Y(M)+SU*Y(NJ):NEXT M 110 FOR P=1 TO 4:LET X(P)=T(P):LET Y(P)=K(P):NEXT P:NEXT N:NEXT J:NEXT I 115 RANDOMIZE USR 50450 120 PAUSE 300 130 CLS 210 LET SU=.1:LET RU=1-SU:LET II=1:LET C=1 220 FOR J=0 TO 3:LET II=-II:LET JJ=1:FOR I=0 TO 4:LET JJ=-JJ:IF I4-J THEN GO TO 310 230 IF J<2 OR I>2 THEN LET C=(C- INT (C/3)*3)+1 240 IF J=3 THEN LET C=(C- INT (C/3)*3)+1 250 LET X(1)=0:LET X(2)=39:LET X(3)=78:LET Y(1)=0:LET Y(2)=-48:LET Y(3)=0:IF II=JJ THEN LET Y(2)=48 260 FOR N=1 TO 11:LET X1=3+X(3)+I*39:LET Y1=160-Y(3)-J*48+II*JJ*24 270 FOR M=1 TO 3:LET X2=3+X(M)+I*39:LET Y2=160-Y(M)-J*48+II*JJ*24:LET C=(C- INT (C/3)*3)+1 280 PLOT X1,Y1-39:DRAW (X2-X1),((Y2-30)-(Y1-30)):LET X1=X2:LET Y1=Y2:LET NJ=(M- INT (M/3)*3)+1 290 LET T(M)=RU*X(M)+SU*X(NJ):LET K(M)=RU*Y(M)+SU*Y(NJ):NEXT M 300 FOR P=1 TO 3:LET X(P)=T(P):LET Y(P)=K(P):NEXT P:NEXT N 310 NEXT I:NEXT J 315 RANDOMIZE USR 50450 320 PAUSE 300 330 CLS 410 LET SU=.2:LET RU=1-SU 420 FOR J=0 TO 2:FOR I=0 TO 2:IF J=0 AND I <>1 THEN GO TO 510 430 LET E=0:IF I=1 THEN LET E=31 440 LET X(1)=0:LET X(2)=25:LET X(3)=75:LET X(4)=100:LET X(5)=75:LET X(6)=25 450 LET Y(1)=31:LET Y(2)=0:LET Y(3)=0:LET Y(4)=31:LET Y(5)=62:LET Y(6)=62 460 FOR N=0 TO 20:LET X1=25+(X(6)+I*75)*.8:LET Y1=(220-Y(6)-J*62-E)*.9 470 FOR M=1 TO 6:LET X2=25+(X(M)+I*75)*.8:LET Y2=(220-Y(M)-J*62-E)*.9 480 PLOT X1,Y1:DRAW X2-X1,Y2-Y1:LET X1=X2:LET Y1=Y2:LET NJ= INT (M-6* INT (M/6))+1 490 LET T(M)=RU*X(M)+SU*X(NJ):LET K(M)=RU*Y(M)+SU*Y(NJ):NEXT M 500 FOR P=1 TO 6:LET X(P)=T(P):LET Y(P)=K(P):NEXT P:NEXT N 510 NEXT I:NEXT J 515 RANDOMIZE USR 50450 520 PAUSE 300 530 CLS 540 GO TO 1 ```