She looked at me through the bus window as the vehicle moved toward the harbour gate where I was standing. Like most of the other passengers, she was wearing a surgical mask and a red-and-black tracksuit top. Our eyes met. She seemed surprised, then, quickly, as if she had recognised an old friend, she waved at me. The other passengers behind her, among them teenagers and young men, echoed the gesture, even though they hadn’t seen her.

I waved back. Hello. You’re safe. Go in peace. Goodbye.

Unspoken words kept shifting in my mind. So many things I wanted to say, but perhaps we would not have shared a language to understand each other anyway. In the end, those gestures – simple, immediate, almost instinctive – were enough. The bus turned and disappeared from view. An ambulance and a short convoy of cars from the Italian authorities followed. I began to cry and hugged two Emergency volunteers from a local group, standing beside me. Like me, they were crying too. In that instant, something clicked inside me, something tore open, something stirred, something that had been asleep or perhaps buried under layers of anger, fear, and anxiety. That gaze made me feel human again.

Allow me to give you more context, because this wasn’t the bus of an identically clad and heavily escorted sports team. The people on the bus were 68 migrants (61 men, 7 women) saved during two distinct missions from the waters of the Libyan SAR (Search and Rescue) zone by the humanitarian vessel Life Support, operated by the Italian independent and neutral NGO Emergency. The migrants were on two overcrowded, unseaworthy rubber dinghies, without safety equipment. Among them there were 18 minors (only 2 of them with their parents, the others were unaccompanied) and one pregnant woman. Their nationalities varied: Bangladesh, Somalia, Sudan and South Sudan, regions shaped by conflict, poverty, and climate stress. The Italian authorities designated Ortona as safe port, 745 nautical miles away from the point of rescue, adding four days of sailing for the survivors. This is by now a consolidated practice criticised by NGOs. The latter claim the Italian government is intentionally directing rescue ships to distant ports to discourage them from staying active in the central Mediterranean. Sailing to a far-off port means prolonging the trauma and stress of survivors, but also spending thousands of euros on fuel and keeping the vessel away from the SAR zone, leaving it exposed to the so-called Libyan Coast Guard, which continues to carry out interceptions and unlawful pushbacks. The Italian Interior Ministry usually remarks to such accusations that spreading arrivals across different regions helps avoid overwhelming key landing points like Lampedusa.

A Search and Rescue mission in the Mediterranean is a delicate operation: the search phase is long and exhausting as spotting dinghies and reaching those on board can be extremely difficult. NGO vessels are also often shadowed by unidentified boats or by units of the Libyan Coast Guard. Conducting rescues in the central Mediterranean is therefore becoming increasingly challenging.

The story of the Life Support is one of hope: since 2022, it has carried out 43 missions and rescued over 3,500 people (at the time of writing this piece). The vessel, which can accommodate up to 175 rescued passengers in addition to its 28 member crew, stands out for its onboard medical team, including two nurses and a doctor. Each person’s health is assessed using triage methods similar to those used by Emergency in its hospitals and medical facilities in war zones and regions affected by conflicts, and their well-being is continuously monitored throughout their time on board. In the spirit of the NGO, that has been providing free, high-quality care to people affected by conflict and poverty since 1994, the ship’s hull bears a quote by the late Gino Strada, surgeon and founder of Emergency: “Rights belong to everyone, otherwise call them privileges.”

The vessel, measuring 51.3 metres in length and 12 metres in width, is also a striking example of healthcare design in action. It offers all the essential features of a rescue ship, while also housing a fully equipped clinic, compact spaces and modular, shared environments. The livery of the ship was redesigned by architect Raul Pantaleo and his studio TAMassociati (some may remember them for the Italian Pavilion at the 16th International Architecture Exhibition). Not a “starchitect,” but an expert in designing for healthcare in challenging contexts, and in creating structures with lasting impact in terms of sustainability, community building, and social equity, Pantaleo tested the symbolic and functional impact of their design firsthand by joining a mission with Emergency in 2023. In his book Architetture del noi, he recounts the mission and describes the ship as “a floating object that can become a political subject, defending and demanding rights and care.”

Design can help, but it cannot solve the migration crisis. Sea crossings remain among the deadliest routes. According to the United Nations’ International Organization for Migration, more than 1,000 people have died since the beginning of 2026. In 2025, at least 2,185 people died or went missing in the Mediterranean.

Migrants crossing the Mediterranean remain a story of humanity in transit, shaped by fragmented wars and hardened borders. Iranian author Shahram Khosravi defines our times in his book ‘Illegal’ Traveller: An Auto-Ethnography of Borders, as “an epoch of border fetishism”. Indeed, migration continues to be framed as a problem. Even among those Italians who identify as Catholics and who one might expect to be guided by the parable of the Good Samaritan, responses are often deeply divided: “We should help them at home,” “Africa can’t move to Italy,” and similar refrains. Years of political sloganeering, fuelled by fears of cultural replacement, job loss, and insecurity, have built mental barriers that are difficult to dismantle. These narratives are often reinforced by political parties and leaders, who at times respond to a humanitarian emergency with controversial or puzzling measures (see Italy’s migrant detention hub in Albania). Rescue ships themselves have become a point of tension for the Italian government. In 2019, Giorgia Meloni, then leader of the right-wing party Brothers of Italy, now Prime Minister, commented on the case of the Sea-Watch 3. Its captain, Carola Rackete, had defied a ban by docking in Lampedusa with 42 rescued migrants after 14 days at sea. Arrested after a confrontation with a Guardia di Finanza patrol boat during manoeuvres, she was later released (in February 2026, a civil court in Palermo ordered the Italian government to pay the NGO Sea-Watch over €76,000 in damages for the unlawful detention of the vessel in 2019). At the time, Meloni argued in a television interview that NGO ships entering Italian waters without authorization should be intercepted, their crews arrested, and the vessel should be seized and sunk if it violated international law and Italian territorial waters.

Such perceptions are not helped by the fact that, at times, suspected migrant smugglers have been identified among those rescued. A 34-year-old man from Sudan was found in possession of a GPS device among those brought ashore in Ortona and was alleged to be a smuggler (the investigation continues at the time of writing this piece). There have been other cases: another suspect, again from Sudan, arrived on board the Life Support in December 2024, docking in Ancona; and in March 2026, three Egyptian men on board the Ocean Viking, a humanitarian SAR vessel operated by the European maritime organization SOS Mediterranee,  also arriving in Ancona, were initially suspected of facilitating irregular migration. In their case, however, the charges were dropped, as they had not received any payment from passengers who had themselves paid traffickers in Libya.

These situations are often complex and controversial, fuelling tensions and feeding criticism of organisations involved in rescue operations. Yet the reality is rarely clear-cut. For ten years, Alaa Faraj, a 31-year-old Libyan man, has been held in Palermo’s Ucciardone prison on charges of multiple counts of manslaughter and aiding illegal immigration, as he is believed to have been one of the migrant smugglers involved in the shipwreck that, in August 2015, caused 49 deaths. Faraj, who has always maintained his innocence, was 20 years old and in his first year of engineering when he left Benghazi, his hometown, and boarded a rubber dinghy to flee the civil war and pursue his dream of becoming a footballer in Europe.

The sea can be scary, unpredictable and merciless. Muddy waves carried the Life Support toward its designated docking area in the early morning of the last day of April, four days after the rescue. The smell of fish hung in the cold air as fishermen in bright orange gear unloaded their catch in the drizzle. The Life Support entered the harbour of Ortona, escorted by a patrol boat of the Guardia di Finanza. Waiting on the dock were teams from the Italian Red Cross, the Italian police and coast guard, the Port, Airport and Border Health Offices (USMAF), and Frontex monitors in their azure identification vests.

The stories of rescued migrants offer a stark, often harrowing glimpse of what unfolds at sea and along the routes leading to it. The group of migrants who landed in Ortona recounted to staff that they had spent days at sea after months marked by violence, detention, and deprivation. One survivor from Sudan, now in its fourth year of war and at the centre of a deepening humanitarian crisis, told the Emergency team on board of imprisonment, mistreatment, and forced labour across multiple countries, before boarding a rubber dinghy that they had to inflate themselves along the Libyan coast. For years I wrote about fashion, and my mind drifted to red carpets, glamorous outfits, paparazzi, to how we talk about pushing and breaking boundaries in fashion. Here, too, there was a crowd, waiting for a group of people in brand-new tracksuits, but with no wardrobes, with nothing. They had crossed boundaries, yet there was no prize waiting for them.

The sea can be fascinating, inspiring, invigorating. Two days before the Life Support arrived in Ortona, Chanel’s Cruise show unfolded in the seaside town of Biarritz. Matthieu Blazy’s first Cruise collection was an ode to the sea, the beach and the coast. There was a gargantuan straw bag, for those wealthy enough to carry it empty, the unburdened privilege of having nothing to carry because somebody else is carrying whatever you need for you.

There were black, gold, and silver heel caps, not quite shoes, just shells for the heel, fastened with thin straps around the ankle, a divisive look built to create debate and clicks. There were oversized, rubberized, thigh-high playful and impractical fisherman’s waders for people who will never fish. Translucent sequins shimmered across evening dresses for would-be mermaids; sailor stripes and beach-umbrella prints evoked an idealized coast. Fishnet layered over newspaper prints, embroidered with fish, evoked newsprint used to wrap fresh catch, while fish-shaped buttons gave a whiff of Schiaparelli’s whimsical buttons.

The dichotomies were striking, or maybe simply unsettling. How curious that in fashion, breaking boundaries with a heel shell is called genius, while in real life crossing borders to stay alive is called a crime. In one world, it is audacity; in the other, it is transgression and ultimately criminalised.

“Teach your children / that the earth is one body / that borders are an invention,” writes Haidar al-Ghazali, a 22-year-old poet from Gaza who last year arrived in Italy where he is currently continuing his university studies. As we waited for the Life Support at the harbour in Ortona, there were many boundaries that I, along with the Emergency volunteers from a local group who had come to greet the crew, could not cross, limits established by the authorities that we naturally had to respect for health and safety reasons. Yet, when the bus carrying the survivors pulled away from the dock, those boundaries seemed to dissolve. Behind the gesture of a stranger who had survived, I was reminded that behind numbers there are people, faces, eyes, lives. Behind statistics there are stories of human beings who defied death, and of other human beings who chose to rescue them. Waving, she signalled that she was alive and grateful; her eyes seemed to say: “I am not the detritus of humanity. I am humanity.”

Emergency is celebrating its birthday on May 15 with a fundraiser. You can contribute at this link.

Carnival season culminates today with Mardi Gras, a joyful celebration of fun and self-expression. Yet as we look at the news there isn’t much to be joyful about, so let’s mark the day with a painting that captures the aftermath of a carnival scene: “Scène de Carnaval” by Alexis Vollon (1889). This monumental piece debuted at the 1889 Salon in Paris, where it was awarded a second-class medal. The painting presents a scene from the Commedia dell’arte, featuring three iconic characters: Pierrot, Colombine, and Polichinelle.

Finding original and intriguing sounds for a runway show can be challenging, but not impossible. One approach is to explore unconventional, abstract, and even alien-like sounds (and noises…), such as those inspired by Earth’s magnetic field.

Around 41,000 years ago, during what is known as the Laschamp event, Earth’s magnetic field briefly reversed and significantly weakened to just 5% of its current strength. This allowed more cosmic rays to reach our atmosphere.

Using data from ESA’s Swarm mission (a trio of satellites launched in 2013 to study Earth’s magnetic signals stemming not only from Earth’s core, but also from the mantle, crust and oceans, as well as from the ionosphere and magnetosphere) scientists from the Technical University of Denmark and the German Research Centre for Geosciences transformed this ancient event into sound. By mapping the movement of Earth’s magnetic field lines during the Laschamp event, they created a stereo soundscape, incorporating natural noises like creaking wood and falling rocks. The result is a mix of familiar and eerie, otherworldly tones.

This process of converting scientific data into sound is similar to composing music from a score. It’s a fascinating fusion of art and science, demonstrating how data-driven compositions can create unique, immersive experiences that can be inspiring also as an unexpected soundscape for a fashion runway.

But the search for experimental music that may be used as the soundtrack of a fashion runway doesn’t stop at planetary sonifications. Tomorrow, at the Munich Kammerspiele, Sharper Than A Needle will take this concept in a different direction. This interdisciplinary project – the world’s first “textile machine orchestra” – transforms sewing machines into synthesizer-like instruments, embedding inside them oscillators and sensors to turn stitching into sound.

Created by artists Stephanie Müller and Klaus Erika Dietl, with collaborators including Karen Modrei, Lisa Simpson, and Stefan Wischnewski, the performance is not a typical concert but a sounding textile workshop. Here, a sewing machine choir harmonizes with the silky whirr of a spinning wheel, a knitting machine pulses with electronic rhythms, and an oversized sewing box becomes a beat machine. Accompanied by video projections that magnify the mechanical choreography, the soundscape is translated into movement, merging fashion, music, and performance into a singular, immersive experience.

Initiated by Stephanie Müller and Klaus Erika Dietl, the minds behind projects like SEWICIDE, beißpony, and the international collective ALLIGATOR GOZAIMASU, Sharper Than A Needle is an interdisciplinary event at the crossroads of textile art, experimental pop, and sound art. For years, Müller and Dietl have explored the intersection of craft and music, using textiles as a tool for networking and creative expression, often within queer-feminist contexts. Through their unconventional performances, they challenge production conditions while crafting multi-sensory experiences. 

The convention is a collaborative effort, featuring Lisa Simpson (aka Agente Costura), Karen Modrei, and Stefan Wischnewski from the Dressed In Sound ensemble. Together, they will explore the acoustic potential of textile machines, turning sewing machines, scissors, needles, spinning wheels, knitting machines, and haberdashery into musical instruments.

With the support of guest artists, the stage will host around 20 performers, including wheelchair dancer Sema Schäffer, percussionist and dancer Ángela Muñoz Martínez, noise sculptor Max Weisthoff, experimental filmmaker Dafne Narvaez Berlfein, and textile artists from the Beyond Textiles network. Additional technical refinements come from Thomas Mayer (aka residuum) and Fabian Zweck.

One of the most striking elements of the performance is the dynamic transformation of costumes: performers such as Schäffer and Muñoz Martínez will wear garments that evolve throughout the show; some costume elements will even be sewn live on stage, blending dance, movement, and textile creation into a single artistic act, where fashion and sound become one.

Müller and Simpson began creating music with sewing machines around 2004, but it wasn’t until ten years later that they finally met and started performing together as a sewing machine duet. Shortly after forming their partnership, Müller invited her frequent collaborator Dietl to join in. Originally a painter, Dietl now uses haberdashery as a tool for sound creation, amplifying for example the sound of threading a needle.

At one of their gigs, some audience members expressed a desire to try out the machines, while others asked for small repairs to their clothes. This shift inspired a new kind of performance, where an extra machine was made available for anyone who wanted to participate, and people could bring their clothes for repairs (something that calls to mind the power of repairing a garment as seen in Lee Mingwei’s The Mending Project).

Tomorrow’s performance will be their largest project yet, with performers on stage using a variety of machines and devices. According to the artists involved, the project also serves as a response to the male-dominated realm of experimental music, and at the same time offers a critique of the exploitation and homogenization within the fashion industry.

You can bet that sooner or later, we’ll see these experimental performers enlisted by fashion houses during a runway show. In the meantime, if you’re seeking unconventional sounds for a runway show, consider these sonic landscapes: from the magnetosphere to sewing machines, these experimental sounds redefine what a fashion soundtrack can be, transforming raw data or industrial rhythms into avant-garde compositions fit for a unique runway show.

Last week, we explored the principle of self-similar scaling in art and fashion, though we left accessories out of the discussion. Milliner Stephen Jones, however, offers us the perfect opportunity to revisit this concept with a piece from his recently unveiled A/W 25 collection.

Entitled “SENSEational” the collection looks at the sensory connections between hats and the body. This thematic interplay is evident in striking contrasts such as a mohawk-style headpiece adorned with sharp Perspex spikes that seem almost dangerous, juxtaposed to an entirely edible, tempered chocolate top hat crafted by Paris-based pastry chef Jana Lai. The latter took inspiration from “Stephen Jones, Chapeaux d’Artiste,” an exhibition at the Palais Galliera. Sound also finds its place in the collection, represented by a gold headphone tiara with feather insulation, besides, since the olfactory experience is gaining momentum through multisensory exhibitions, scent is explored through hats infused with fragrances like Wonderwood by Comme des Garçons or Tweed by Lenthéric.

Among the most architectural designs of the collection there is a hat structured with floating concentric mirror panels reminiscent of planetary rings in a gradually decreasing triangular configuration. Encircling the head and partially veiling the face, the piece invites comparisons with buildings such as Yanlord Central Lake by HWCD & TIANHUA, in Taicang, China, designed to resemble ripples in water and forming a spiral form, as well as to architecture-inspired spiral hats. It also echoes the geometric, avant-garde attire of the Queen of Mars in Yakov Protazanov’s 1924 sci-fi film Aelita. Yet, its true inspiration lies elsewhere, Stephen Jones conceived indeed the design as an homage to the late Italian fashion writer Anna Piaggi.

Named “Positive Vibes,” this cocktail hat references Piaggi’s own musings that she wore hats to keep her thoughts from escaping (an idea that intriguingly contrasts with Italian actress Valentina Cortese’s reason for wearing scarves, which she saw as both a tribute to the farming couple who raised her and a way to shield herself from intrusive thoughts…). Here, self-similarity transcends pure mathematics or architecture, taking on a conceptual, almost philosophical dimension, an elegant fusion of form, function, and meaning.

Following our previous explorations of geometric interplay, let's draw inspiration from a work rooted in geometry and machines – Andor Weininger's sketch for his experimental project "Mechanische Bühnen-Revue" (Mechanical Stage – Abstract Revue). This piece will be featured in "Masterpieces on Paper from Budapest," an exhibition at the Guggenheim Museum Bilbao, Spain (February 28th – May 25th, 2025). Organized in collaboration with the Museum of Fine Arts – Hungarian National Gallery of Budapest, the exhibition presents works spanning from around 1400 to the present day, offering a rare chance to see pieces that are typically only available in specialized publications or temporary exhibitions.

Born in 1899 in Karancs, Hungary, Andor Weininger was the son of a musician. He initially studied law in Pécs before switching to architecture at Budapest's Technical School. His studies were interrupted by World War I, and after a brief period in Munich, he suffered another setback following his father's death. In 1921, his artistic path led him to the Bauhaus in Weimar, where he trained in the mural painting workshop under Oskar Schlemmer and Wassily Kandinsky. A passionate musician, Weininger also founded the Bauhaus Orchestra in 1924, known for its experimental instruments and avant-garde compositions.

After leaving the Bauhaus in 1925, Weininger returned to Dessau in 1926 to work in the Department of Architecture, a period during which he developed his Kugeltheater project. Following his departure from the Bauhaus in 1928, he pursued independent work in Berlin before emigrating first to the Netherlands in 1938, then to the United States.

Weininger's artistic journey was deeply influenced by his interactions with avant-garde figures, particularly Oskar Schlemmer. Both artists explored the dehumanization of the body in performance, but Weininger's Marionettentheater and Mechanische Bühnen-Revue pushed this idea even further. His experiments with movement, geometric abstraction, and symbolic transformation drew from avant-garde puppetry, particularly Edward Gordon Craig's "Übermarionette," where movement was controlled mechanically rather than through human actors.

The themes of automatons and robots, particularly within theater, are central to Weininger's work, where craft and industrial elements merge. His theater sought to dismantle conventional forms, embracing the experimental energy of the avant-garde.

Developed in the early 1920s at the Bauhaus in Weimar, "Mechanische Bühne-Revue" was closely tied to the school's broader explorations in stage design. Weininger envisioned a performance space where human presence was minimized or even eliminated, aligning with contemporary ideas of mechanized art. While his work ran parallel to Oskar Schlemmer's Bauhaus theater experiments, it was not merely derivative. Schlemmer stylized human movement within geometric costumes, while Weininger's vision extended beyond the human body, shifting toward a purely mechanical performance.

In "Mechanische Bühnen-Revue" (Mechanical Stage Revue) performance, movement, and abstraction converged. Elements of popular performative genres were fused with Bauhaus principles of color, shape, and motion, culminating in a complex, synchronized spectacle of light, form, and mechanical figures unfolding on stage. Weininger's design introduced a dynamic stage, where elements were supposed to move in multiple directions and surfaces shifted, evoking perspective through a moving point of confluence, disrupting the conventional picture frame. This reimagined stage, reminiscent of De Stijl compositions, rejected the constraints of the traditional proscenium.

This approach placed "Mechanische Bühnen-Revue" at the forefront of kinetic stage design, pushing beyond Schlemmer's reliance on dancers and instead presenting an abstract, mechanized spectacle. Geometric shapes and color compositions, influenced by Theo van Doesburg and Russian Constructivism, underscored the stage's engineered dynamism. Echoing Lissitzky's "Victory Over the Sun" and Lyubov Popova, and Vsevolod Meyerhold's biomechanical experiments for "Le Cocu magnifique" by Fernand Crommelynck (think about Popova's set that wasn't a traditional backdrop but a dynamic, functional structure made of industrial materials such as ladders, wheels and conveyor belts), Weininger imagined a performance space in perpetual motion, with rotating elements and mechanized transitions that anticipated later developments in multimedia performance and cybernetic theater.

Though less widely recognized than Schlemmer's "Triadic Ballet", Weininger's contributions remain a vital part of Bauhaus theater history, reflecting the era’s fascination with the synthesis of humans, machines, and performance into a singular artistic language. His vision may inspire not only stage design but also fashion, particularly in the use of mechanized elements in fashion shows. In an age of increasing mechanization, will we see one day a fully robotic runway? After all, while puppetry has made its way onto the catwalk (think about 1960s runways with puppets as models, Moschino's puppet presentation for the house's S/S 21 collection or KidSuper's models-turned-puppets in his S/S 25 show), a completely automated fashion show has yet to materialize. Food for thought.

At the end of yesterday's post, we mentioned Benoît Mandelbrot, the Polish-born French mathematician renowned for his groundbreaking work on fractal geometry. Today, rather than exploring other ideas, let's take a moment to relax and find inspiration in one of his most influential works, The Fractal Geometry of Nature (Download TheFractalGeometryofNature).

First published in 1982, The Fractal Geometry of Nature is an expanded and revised version of Mandelbrot's 1977 book Fractals: Form, Chance, and Dimension, which itself built upon his earlier 1975 French work Les Objets Fractals: Forme, Hasard et Dimension. In this seminal book, Mandelbrot introduces the concept of fractals, demonstrating how the intricate patterns and structures found in nature can be understood through fractal geometry.

One of the book's most striking contributions is its demonstration of how fractals naturally emerge in a wide range of phenomena. Mandelbrot provides numerous real-world examples, such as the branching patterns of trees and blood vessels, the jagged edges of clouds and mountain ranges, the clustering of galaxies in the universe, and the structure of river networks and lightning bolts. By exploring these examples, Mandelbrot reveals that the complexity of nature follows simple, self-replicating rules.

In his volume Mandelbrot challenges traditional Euclidean geometry, which relies on smooth, idealized shapes like spheres, cubes, and lines. He argues that these classical forms fail to capture the roughness and irregularity of the real world. Instead, fractal geometry provides a mathematical framework that embraces the complexity of nature, offering a new way to model and understand it.

A defining characteristic of fractals is self-similarity, meaning their structure remains consistent at different levels of magnification. Mandelbrot explores how fractal scaling laws apply to both natural and artificial systems, challenging the assumption that smoothness and uniformity are the default.

Even as technology progresses and computer-generated fractals grow increasingly detailed, The Fractal Geometry of Nature remains an essential and fascinating exploration of the hidden mathematical order in the world around us. Its influence extends beyond mathematics, shaping fields such as physics, biology, economics, and, last but not least, art. Mandelbrot's insights continue to inspire scientists, artists, and thinkers, proving that simple rules, when repeated endlessly, can give rise to boundless complexity and beauty.

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."

In the latest posts, we explored mathematical principles and fractal-like patterns. Today, let's put those inspirations into practice by creating something inspired by geometry – an origami paper lamp with a diamond pattern. The instructions come from a vintage French magazine, Echo de la Mode (19th – 25th November 1967). Enjoy!

MATERIALS

Two sheets of Bristol paper (350 g) measuring 65 × 60 cm; eight 3 × 3 mm balsa wood sticks; two 3 × 5 mm of balsa wood sticks; two sheets of tracing paper (90 g) measuring 65 × 50 cm; one 3 × 15 mm poplar wood strip; 1 tube of glue; 1 roll of invisible adhesive tape.

INSTRUCTIONS

On the Bristol paper sheets, mark a point every 4.5 cm across the width and every 4 cm along the length. Then draw triangles with a base of 9 cm (4.5 × 2) and a height of 4 cm.

Cut out 48 simple triangles, 48 triangles with an additional 5 mm strip on one of the sides opposite the base (for gluing) and 48 triangles with a 5 mm strip on the sides opposite the base.

Take one triangle of each type and apply strong glue to each 5 mm strip. Then glue the three triangles together to form a pyramid.

Trim two of the three tips of your pyramid to allow a 34.5 × 0.5 cm balsa wood stick to pass along one of the edges (see drawing A).

Glue your pyramids onto the balsa stick, leaving a 2.5 cm gap between them, meaning three pyramids per stick (see drawing B).

The first pyramid starts at one end of the stick. Let it dry. Then glue the sticks onto a wooden frame measuring 30 × 25 cm. The corner sticks should extend downward, while the central ones should point upward. Reinforce the frame with a 30 × 1.5 cm flat wooden strip. Once the structure appears sufficiently dry, glue the frame onto the tracing paper, which you will have previously stretched and secured with thumbtacks onto a drawing board.

Using a razor blade, cut away any excess tracing paper. Then join the four elements with invisible adhesive tape. To reinforce the entire structure and allow it to be hung, create a solid frame for your lantern by making a cross support out of poplar wood (see drawing C).

In yesterday's post, we explored the concept of self-similarity in art, science, and fashion. This discourse extends into architecture, where certain structures, often less immediately apparent, exemplify this principle, such as those designed by Paolo Portoghesi.

An admirer of Baroque architect Francesco Borromini, Portoghesi deeply studied his work, particularly Borromini's mathematical approach to spatial design and geometric manipulation. This influence is evident in Portoghesi's own architectural language, where he sought to create dynamic and responsive spaces. 

While Borromini may not have explicitly engaged with self-similarity in the modern mathematical sense, his use of proportional relationships and recursive geometric systems exhibits its defining characteristics. Self-similarity, in essence, refers to patterns that repeat at different scales, a principle clearly observed in Borromini's manipulation of geometric forms and proportions.

In buildings like San Carlo alle Quattro Fontane, Borromini used geometric transformations that involved recurring forms, such as circles and ovals, creating a sense of continuity and harmony. In this church Borromini used recursive geometric subdivisions to create smooth, continuous surfaces. He employed the pantograph to generate flowing curves with different tangents, tracing curves along others. The church's design, both in plan and facade, utilized the column diameters to create an intricate balance of concave and convex shapes.

Borromini's approach often involved expanding or contracting shapes in a way that each part of the building echoed the proportions and geometries of the whole, a key feature of self-similarity.

While Portoghesi may not have explicitly framed his architectural approach through the mathematical lens of self-similarity, his use of modularity, geometric repetition, and scaling principles aligns with the essence of self-similarity in architecture. His designs often explored the interplay of forms that echoed one another across different scales, creating a cohesive spatial rhythm and a deep sense of continuity.

A striking example is his design for the Mosque of Rome (1975-1995), where he merged Islamic architectural traditions with contemporary design principles. The mosque's composition is structured around modular repetitions resonating at different scales, repeating geometric patterns and motifs rooted in Islamic art (an architectural language inherently based on self-similarity).

The expansive prayer hall, with its towering, curving pillars, evokes the image of a forest, reinforcing a sense of organic spatial flow. The dome and overall spatial organization employ recursive geometric relationships, mirroring the intricate self-referential structures found in traditional Islamic architecture while integrating a distinctly modern sensibility.

The principle of self-similarity is also evident in Casa Papanice (1969), where concentric circles define both the floor plan and the interior spatial organization. This motif becomes particularly striking for example in the living room ceiling, where a series of overlapping cylindrical forms, radiating from multiple focal points, reinforce a layered sense of depth and continuity. The geometrical forms in this building offer spatial dynamism and fluidity.

A similar approach can be observed in the Chiesa della Sacra Famiglia (Church of the Holy Family, 1969-74) in Salerno, where the circle serves as a recurring architectural motif, symbolizing unity and eternity. The circular plan and dome-like roof establish a sacred spatial order, creating a dialogue between structure and worshippers while emphasizing the completeness and continuity of the space.

For fashion designers Portoghesi's plans may also be intriguing and inspiring for embellishments and embroideries, in particular the diagrams from his "Fields Theory" (Teoria del campi), a concept he formalized in Inibizioni dell'architettura moderna (1974).

Drawing inspiration from the intricate ornamentation of Baroque altars, Portoghesi proposed that architectural elements could generate spatial waves similar to magnetic fields affecting their surroundings through intensity, light, and sound. This idea materialized in a series of very inspiring spatial diagrams (View this photo) composed of concentric ripples resembling waves illustrating the dynamic interplay between built form and its environment that then inspired a series of projects that culminated in Casa Papanice and the Church of the Holy Family.

A recent study published on the journal PNAS Nexus in early February, titled “Scaling in Branch Thickness and the Fractal Aesthetic of Trees,” reveals that trees depicted in paintings by renowned artists like Leonardo da Vinci and Piet Mondrian follow the same mathematical laws of natural branching as real trees.

In nature, trees exhibit a self-similar branching pattern, meaning the same structures repeat at progressively smaller scales from the trunk to the branch tips.

In the study, scientists mathematically analyzed the scaling of branch thickness in artistic depictions of trees. Leonardo da Vinci, whose guidelines for painting trees have influenced both artists and scientists, described this scaling with a parameter called α (the radius scaling exponent). He proposed that if a branch’s thickness equals the combined thickness of its two smaller branches, then α = 2.

Applying da Vinci’s ideas to famous artworks, researchers measured α and compared it to real trees. They found that α in paintings ranges from 1.5 to 2.8, similar to natural trees. While some artworks adhere to this pattern, others deviate intentionally for artistic effect or due to stylistic constraints.

The study examined trees in art from around the world, including the intricate tree patterns carved into the stone window screens of the late-medieval Sidi Saiyyed Mosque in Ahmedabad, India; Cherry Blossoms, an ink-on-paper painting by Matsumura Goshun (1752–1811) from Japan’s Edo period and Gustav Klimt’s L’Arbre de Vie (Tree of Life), a celebrated work known for its decorative, spiraling branches.

Even in abstract works like Piet Mondrian’s De Grijze Boom (Gray Tree, 1912), where the branches are portrayed as abstract clusters of dark arcs instead of traditional tree-like colors, some scaling in branch thickness still exists. Despite the lack of typical tree representation, these arcs symbolizing parts of the branches allowed the researchers to analyze the overall structure of the tree. This suggests that when artists, even unknowingly, use a mathematically based value for α, the human brain still recognizes the image as a tree.

To further explore this idea, Mondrian’s later painting, Bloeiende Appelboom (Blooming Apple Tree, 1912), removes even the scaling of branch diameter. The result is that the “tree” effect vanishes. Without the natural variation in branch thickness, Blooming Apple Tree could just as easily be interpreted as dancers, fish, flowers, or a purely abstract composition.

The study implies that incorporating realistic branch scaling into art enhances our ability to identify tree depictions. This opens up new ways to appreciate both nature and art, while also offering fresh perspectives on the beauty of trees in both contexts. Moreover, it emphasizes how various forms of artwork, whether traditional carvings or abstract paintings, can be analyzed using scientific methods to reveal hidden patterns in the portrayal of nature.

This brings us to an interesting parallel: fashion, much like art, is shaped by mathematical principles – think measurements, patterns, and sizes. So, could the concept of self-similarity inspire a mathematical approach to fashion design? Yes as the principle of self-similarity could be used to create layers that follow a specific progression, generating a sense of continuity and flow in designs. However, it’s crucial to distinguish between self-similar scaling and graduated or tiered designs, as these two concepts serve different purposes in shaping visual harmony.

Self-similar scaling refers indeed to a pattern where each part is a smaller version of the whole, often following a mathematical ratio. It’s the same principle seen in nature, such as the branching of trees or the structure of Romanesco broccoli, a fractal vegetable where each smaller part mirrors the whole, no matter how much you zoom in or out, adhering to a consistent ratio. On the other hand, graduated or tiered designs involve a structured arrangement where elements change in size, but they don’t necessarily follow a strict proportional rule.

So, in nature, self-similar scaling follows a power law, where each segment is reduced by a consistent ratio, commonly ½ or ⅔ of the previous one. Applied to fashion, this concept requires precision, as it is easy to mistake a tiered or layered design for a self-similar one.

For instance, stacking seven shirts with progressively shorter sleeves does not create a self-similar pattern; rather, it results in a graduated or stacked effect without a strict proportional relationship. True self-similar fashion structures must adhere to a recursive scaling principle, where each element is a mathematically scaled-down iteration of the previous one, forming a continuous system rather than independent layers.

So remember, a self-similar design is characterized by strict proportionality, if each layer is exactly 70% or 50% of the preceding one, it meets the mathematical criteria. However, if proportions vary based on aesthetic preference rather than a precise ratio, the result is a graduated rather than a self-similar composition.

Consider, for instance, Cinzia Ruggeri’s costume for Valeria Magli’s Banana Morbide an example of a graduated design. The costume is made of multiple thin tops with one progressively shorter sleeve stacked one on top of the other, but the sleeve does not follow a strict mathematical sequence. Capucci’s 1956 Nove Gonne (Nine Skirts) dress could theoretically approach self-similarity, as it is a single-piece garment with diminishing layers. Yet, its asymmetrical structure, shorter in the front, longer in the back, reveals that Capucci’s methodology leans toward sculptural volume. In a nutshell, the design explores architectural repetition, but the scaling is more intuitive than formulaic.

For purer examples of self-similarity in fashion, we must look to designers who embrace mathematical rigor, such as origami-inspired couture. Some of the “haute papier” creations from Sandra Backlund’s “Ink Blot Test” collection (A/W 2007–08) and Bea Szenfeld‘s “Sur La Plage” (2010) demonstrate the recursive logic of fractal-like structures, creating a mesmerizing visual effect. Two designs from these respective collections, with their progressively diminishing shapes, create an intricate, almost hypnotic, self-similar texture.

So, from now on, try to spot more examples of self-similarity in fashion. Exploring this concept sharpens our aesthetic awareness and pushes the boundaries of garment construction, challenging us to construct garments with the same mathematical harmony and rhythm that nature so effortlessly achieves in its patterns.