Case Study: Canvas-015

Module 1: Metadata Table

Property	Specification
Canvas ID	Canvas-015
Perception	Inclusiveness
Structure	Line Composition & Interlocking Squares
Syntax Type	Vertical & Horizontal Cyclic Pattern
Thread Specs	DMC Floss / Size 25, 4 strands folded
Color Palette	Dark Green (#1e5e3a), Light Green (#82c496)
Stitch Direction	Begins from the central light-green 2×2 square, establishing fixed square boundaries. Starts via stair-like 5×5 ladders on both sides.

Module 2: Starting & Vector Operations Algorithm

The structure of Canvas-015 consists of three 10×10 grid blocks (Block 1, Block 2, Block 3) replicated through diagonal translational shifts (ΔX, ΔY) = (+3, +3), yielding a total of 228 stitches (76 stitches per block). Diagonal lines serve as the fundamental framework of Canvas count-stitching.

Phase ①: Block 1 (Stitches 1–76, 10×10 Grid)

• Origin Coordinate: (140, 100)
• 1. Blue Diagonals & Yellow Turns (Stitches 1–18):
  • Stitches 1–10, 13–18: Diagonal from top-left to bottom-right, vector (Δx, Δy) = (+1, +1), angle θ = -45°, length L ≈ 5.1 mm (1-grid diagonal).
  • Stitches 11–12: Transition to yellow stitches acting as directional turning pivots.
• 2. Pink/Red Vertical & Horizontal 1-Grid Diagonals (Stitches 19–56):
  • Stitches 19–40: Top-left to bottom-right 1-grid diagonals (Δx = +1, Δy = +1), angle θ = -45°, length L ≈ 5.1 mm.
  • Stitches 41–56: Bottom-left to top-right 1-grid diagonals (Δx = +1, Δy = -1), angle θ = +45°, length L ≈ 5.1 mm. Forms the frame boundaries.
• 3. Green 3-Grid Long Span Diagonals (Stitches 57–76):
  • Stitches 57–76: Top-right to bottom-left 3-grid long spans (Δx = -3, Δy = +3), angle θ = 135°, length L ≈ 15.1 mm.

Phase ②: Block Replication & Shift Operations

• Block 2 (Stitches 77–152): Replicates Block 1’s path and colors, shifted by vector (ΔX, ΔY) = (+3, +3) grid units. Starting origin shifted to (200, 160).
• Block 3 (Stitches 153–228): Replicates Block 1’s path again, shifted by vector (ΔX, ΔY) = (+6, +6) grid units. Starting origin shifted to (260, 220).
• Geometric Result: 36 light-green 2×2 units interlaced with dark-green background stitches form a cyclic pattern of 6 vertical units on the right and 6 horizontal units on the left, embodying “Inclusiveness.”

Module 3: Structural Mechanics & Topology

1. Structural Spine & Nesting Frames

• Nested Square Spine: Nested square frames combining 2, 3, 4, and 5 grid units provide rigid geometrical support across the entire composition.
• Cyclic Interlocking Nodes: Intersection nodes of vertical and horizontal alignments securely lock the warp and weft threads of the canvas fabric.

2. Tension Equilibrium & Stress Dispersion

• Orthogonal Force Cancellation: Short 1-grid stitches (θ = ±45°, L ≈ 5.1 mm) generate micro shear stresses that counteract the high tensile forces of 3-grid long spans (θ = 135°, L ≈ 15.1 mm).
• Planar Tension Dispersion: Expanded 4-strand threads fill grid holes completely. The balanced long and short stitches distribute surface tension evenly across the 30×30 grid, suppressing fabric warping and achieving a flat, relief-like surface topology.

Module 4: Vector API & Dynamic Display Data

1. SVG Geometric Parameters

• ViewBox: 0 0 500 500
• Grid System: 20 × 20 unit base grid covering a 30 × 30 grid area.
• Colors & Specs: Dark Green (#1e5e3a), Light Green (#82c496), stroke-width: 3.5, stroke-linecap: round.
• Animation Controls: stroke-dasharray: 60, stroke-dashoffset: 60, single stitch duration 0.4s, sequential delay 0.05s per stitch.

2. Renderable HTML/SVG Code Card

Module 5: Visual Gallery

Front View	Back View	Handscript Diagram
Fig 1: Front View (Interlocking Light and Dark Green Squares)	Fig 2: Back View (Parallel Diagonal Stress Lines)	Fig 3: Original Diagram (Stitch Path & Coordinates 1–228)

Module 6: Algorithm Extensions & Variant Syntax

1. Physical Coverage

• Equation: Coverage = (N × L × W) / A_total
• Evaluation: Multi-layered 4-strand DMC thread layering achieves a high thread coverage rate of 92%–95%, completely concealing the backing fabric and creating a dense, tactile relief structure.

2. Procedural Extension Parameters

JavaScript

const Canvas015_Parameters = {
canvasID: "Canvas-015",
perception: "Inclusiveness",
gridDimensions: { width: 30, height: 30, unitSize: 20 },
threadConfig: { brand: "DMC Size 25", strands: 4, folded: true },
colors: {
primary: "#1e5e3a", // Dark Green
secondary: "#82c496" // Light Green
},
proceduralRules: {
baseUnitStitches: 76,
totalStitches: 228,
stepSequence: ["Center_2x2_Square", "Stair_5x5_Ladders", "Nested_Frames_2_3_4_5", "Outer_3Grid_Spans"],
unitSpacing: { deltaX: 3, deltaY: 3 },
gapRatio: 0.0,
cyclicMode: "Vertical_6_Horizontal_6"
}
};