Case Study: Canvas-008

Computational Embroidery Syntax Card

Property Item	Metadata & Specification Content
Archive ID	Canvas-008
Perceptual Impression	5-4-3-2-1 descending diagonal step array, sharing diagonal tracks to demonstrate geometric gradations and precise interlocking rhythmic movement
Base Structure	Uses diagonal stitches ($45^\circ$) with descending lengths of 5-4-3-2-1 as a fundamental unit, recursively advancing along a shared 1-cell track to the lower-right
Thread Specification	DMC / Size 5 pearl cotton doubled, Size 25 embroidery floss
Colors Used	Dark Gray/Black, Dark Blue, Light Blue, Red (Four-color step interleaved fluid dynamics)
Composition Direction	Recursively advances from top-left to bottom-right; stitches start top-right and drop bottom-left ($45^\circ$ diagonal stitch)

Starting Rules:
- Base Unit (Stitches 1-10, Unit 1):
  - Stitches 1-2 (Span 1 cell): Top-Right $(70, 30) \rightarrow$ Bottom-Left $(50, 50)$
  - Stitches 3-4 (Span 2 cells): Top-Right $(90, 30) \rightarrow$ Bottom-Left $(50, 70)$
  - Stitches 5-6 (Span 3 cells, longest stitch): Top-Right $(110, 30) \rightarrow$ Bottom-Left $(50, 90)$
  - Stitches 7-8 (Span 2 cells): Top-Right $(110, 50) \rightarrow$ Bottom-Left $(70, 90)$
  - Stitches 9-10 (Span 1 cell): Top-Right $(110, 70) \rightarrow$ Bottom-Left $(90, 90)$
- Bottom-Right Recursive Rule (Stitches 11-40, 4 Diagonal Slope Units):
  - Stitches 11-20 (Unit 2): Recursively offsets toward bottom-right by $(\Delta x = +60, \Delta y = +60)$.
  - Stitches 21-30 (Unit 3): Recursively offsets toward bottom-right by $(\Delta x = +120, \Delta y = +120)$.
  - Stitches 31-40 (Unit 4): Recursively offsets toward bottom-right by $(\Delta x = +180, \Delta y = +180)$.
Polar Vector & Angle Operations (Syntax Type: Step-Decreasing Repeating Array):
- Diagonal Vector: Angle $225^\circ$ (Top-Right to Bottom-Left), unit vector directional delta $(\Delta x = -20, \Delta y = +20)$.
- Stitch Length Span: 1 cell ($\sqrt{800}\text{ px}$), 2 cells ($\sqrt{1800}\text{ px}$), 3 cells ($\sqrt{3200}\text{ px}$).
- Gap Offset: Default $0.0$, endpoints precisely locked to grid cell centers $+0.5$.

Core Topological Node Network:
- Interlaces 1-2-3-2-1 length diagonal stitches to form a stepped tension core at the center.
- Units overlap heavily via “shared diagonal tracks” to construct a seamless, highly resilient topological network.
Mechanical Structural Analysis:
- Interlaced Tension Release: Long stitches (3 cells) pull main visual diagonal lines, while shorter side stitches (1 cell, 2 cells) anchor grid nodes to prevent long segments from slackening.
- Diagonal Overlap Stabilization: Double-layered thread accumulation on shared tracks significantly enhances fabric density and abrasion resistance, preventing deformation caused by diagonal tension pulling.

Canvas-008 Computational Embroidery: 5-4-3-2-1 Diagonal Slope Step Array

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SVG Vector Geometry Parameters:

ViewBox: 0 0 320 300
Grid Cell Standard: Grid unit $20\text{ px}$, endpoints precisely located at grid cell center $+0.5$
Base Pattern Span: 1-2-3-2-1 Units
Vector Path Sequential:
- Stitch 1-2: $(70, 30) \rightarrow (50, 50)$ | Length: 1 unit
- Stitch 3-4: $(90, 30) \rightarrow (50, 70)$ | Length: 2 units
- Stitch 5-6: $(110, 30) \rightarrow (50, 90)$ | Length: 3 units
- Stitch 7-8: $(110, 50) \rightarrow (70, 90)$ | Length: 2 units
- Stitch 9-10: $(110, 70) \rightarrow (90, 90)$ | Length: 1 unit (Overlapping track)

Thread Physics & Coverage:
- Mesh Size: 18-count Mono Canvas.
- Coverage & Layering: Four-color step alternating sequence creates high surface coverage and strong dynamic fluid movement.
Stitch Variant Matrix:
- Rhythmic Expansion Variant: The central longest stitch can be extended to 5 cells (forming a 1-2-3-4-5-4-3-2-1 array), greatly intensifying the undulating sensation of the slope.
Procedural Parameters:
- gapRatio: Default is $0.0$, locking endpoints to grid cell center $+0.5$, showcasing the ultimate geometric aesthetics of computational embroidery.