In yesterday's post, we explored a vintage interior design project. Today, let's shift focus to fashion with another piece from the same year and magazine, Echo de la Mode (16th - 22nd April 1967). This time, it's a pointed scarf by Jean-Charles Brosseau, a design that elegantly frames the wearer's face, foreshadowing the sculptural headdresses of Pierre Cardin's 1970 nurse uniforms.
Crafted from organdy and edged with delicate gold or silver beaded trim (1.25 m), this scarf, according to the magazine, was versatile and refined as it paired with any outfit, while embroidered fabric, printed organza, or muslin variations would have allowed for playful customization. A practical touch: two snap fasteners secured it neatly under the chin.
Materials:
• 1 m of organdy (120 cm wide)
• 1 m of silver trim (1 cm wide)
Instructions:
1. Fold the fabric into a triangle for a full bias cut and baste the layers together.
2. Trace the provided pattern at actual size, ensuring proper bias alignment.
3. Cut the fabric, leaving a 0.5 cm seam allowance.
4. Baste and stitch, leaving one end open. Press seams open, turn right side out, then press again.
5. Close the open end and attach the trim with invisible stitches.
Now let's radically transform this project by wondering what if this simple yet elegant accessory were reinterpreted through the lens of mathematics and architecture? By blending computational design, fractal geometry, and structural experimentation, we could transform this basic triangular form into a self-similar fractal structure, shifting from a smooth paraboloid surface to a fragmented, recursive geometry, with each iteration revealing new complexity.
Let's look at this step by step:
1. Start with the Base Shape
• The original scarf has a simple pointed, triangular form; this can be represented as a basic parabolic curve or even a flat polygon.
2. Introduce Midpoint Displacement (Archimedes' Method)
• Apply the midpoint displacement method to the main diagonal edge of the triangular scarf.
• In its classical form (w = 1/4), this produces a gently curved structure resembling a parabola.
• If we adjust w dynamically (increasing it toward 1/2, as Teiji Takagi did), the structure becomes rougher and more self-similar.
3. Refining for Self-Similarity
• To achieve fractal characteristics, apply the midpoint displacement recursively.
• Each new segment is divided again, with its midpoint displaced.
• This creates a scarf edge resembling a Takagi curve, making the outline jagged yet mathematically structured.
• In 3D (applied to fabric draping), this could generate a Takagi mountain-like texture.
4. Material & Construction Considerations
• A slightly stiff fabric (e.g., organza or organdie) would help maintain the fractalized drape.
• Laser cutting could ensure precise fractal edges without fraying.
• Folding techniques, similar to origami structures, could introduce gridshell-like rigidity into the fabric.
5. Dynamic Adjustments Using Parametric Design
• Using Grasshopper (Rhinoceros3D), we could experiment with different w values:
• w = 0.25 → Smooth curves, subtle texturing.
• w = 0.5 → More fractal, rougher edges, enhanced self-similarity.
• w = 1.0 → Maximum roughness, highly jagged and structured.
6. Alternative Approach: Koch Snowflake Influence
• Instead of just midpoint displacement, we could iteratively subdivide and extend the scarf's edges in a Koch curve-like manner.
• This would create a lace-like fractal trim.
Result: A Fractal-Infused Scarf
The final design could feature:
• A pointed scarf with jagged, self-repeating edges.
• A softly structured yet computationally precise textile.
• A decorative (yet not necessarily wearable) piece that embodies geometric complexity.
The listed phases can be seen in two ways, depending on your approach: If you want a structured evolution of the scarf design, you could follow the steps in order, from basic shape to more complex fractal adaptations. In this case, each phase builds upon the previous one, gradually increasing complexity. If you're exploring different ways to reinvent the scarf, you can treat each phase as a separate method.
For example, you could try only Step 2 (midpoint displacement) for a subtly curved design or jump straight to Step 6 (Koch snowflake approach) for a lace-like effect. If you're interested in computational design, Step 5 (parametric adjustments in Grasshopper) might be the main focus. It really depends on how much complexity you want in the final piece and whether you want to experiment with multiple iterations or just one transformation.
AI-assisted modeling could help visualize this metamorphosis, illustrating how an elemental shape can evolve into a multi-layered architectural form (see last image in this post, a DALL-E sketch). Through this process, the scarf transforms from a mere accessory into an exploration of structured complexity, where design and mathematical precision converge. Enjoy experimenting with this transition from simple shapes to intricate forms remembering what Polish-born French mathematician Benoît Mandelbrot stated: "Bottomless wonders spring from simple rules which are repeated without end."
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