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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.

In this aftermath of the party, we can see the remnants of the celebration scattered around the scene, a sign of revelry winding down. Pierrot, with his typical melancholy, declares his affection for Colombine, who appears flattered but possibly uninterested. Meanwhile, in the background, Harlequin, dressed in his trademark diamond-pattern costume, can be seen through a doorway on the right, watching from a distance as he too is in love with Colombine. On the left, Polichinelle (French for the Commedia dell'arte character Pulcinella), is seated, seemingly dozing off, his signature hat discarded beside him. This gesture may symbolize his indifference or detachment from the emotional drama unfolding between Pierrot and Colombine.

The painting brilliantly captures the theatrical tension between Pierrot's earnestness and Polichinelle's playful, indifferent demeanor. Vollon's choice to highlight the interaction between Pierrot and Colombine, with Harlequin observing from afar, creates a layered narrative filled with unrequited love, jealousy, and comic detachment.

Influenced by French Realism, Vollon followed in the footsteps of his father, Antoine Vollon, which is evident in the realistic and detailed portrayal of the characters, despite their exaggerated, theatrical nature. This piece stands as a prime example of late 19th-century French realism, blending dramatic emotion with meticulous attention to costume and character portrayal. Vollon used colors typical of the period, mixing the bright, festive tones of Carnival – reds, blues, and golds – with darker shades to create depth in the characters' emotional complexities. The vivid contrast in their costumes – Pierrot's white blouse, Colombine's red corset, and Polichinelle's bolder yellow and pink ensemble – accentuates their distinct personalities. Polichinelle's costume also features two humps, one on his back and another on his belly. The back hump, comically sagging and almost deflated, mirrors his weary, detached demeanor.

The painting made such an impact that it wasn't just displayed at the Salon, it was also circulated as an etching in Figaro-Salon and L'Art publications in 1890 and 1891, reaching an even wider audience.

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.

In yesterday's post, we looked at a work from the Marcel Lehmann-Lefranc Collection, currently featured in Sotheby's "Contemporary Discoveries" sale. Among the striking pieces in the auction there is also Niki de Saint Phalle's "Tir (Old Master)" (1961), a visceral and performative exploration of destruction as creation.

This piece belongs to her renowned Tirs series, in which de Saint Phalle orchestrated a radical reimagining of the canvas. Constructing layered assemblages of found objects and toys, she would create plaster reliefs. She then enacted a dramatic intervention by firing a .22 Long Rifle at the work itself. The bullets punctured hidden capsules of paint, triggering controlled explosions that released bold, cascading colors across the surface.

Through her Tirs, de Saint Phalle didn't merely paint, but staged a confrontation, transforming destruction into a means of artistic genesis. Rather than extending beyond the canvas like Lucio Fontana, she pierced it, unveiling the latent energy behind the surface, allowing it to spill forward in an unrestrained, almost theatrical spectacle of movement and texture. By inviting spectators to take part in the shooting, she also dissolved the boundary between artist, artwork, and audience, turning passive viewers into active participants in the creative act.

Violence and beauty coexisted in this ritualistic performance. The eruptions of paint, often in vivid, electrifying hues, spilled onto the composition like raw emotion, almost as if the painting itself could bleed. The work featured in Sotheby's sale is particularly striking, bearing visible bullet wounds and rivulets of color that testify to the charged moment of its making. For de Saint Phalle, this act was not just aesthetic but deeply political and personal as each shot fired became both an act of rebellion and a brushstroke of liberation.

"By shooting at myself, I was shooting at society and its injustices. By shooting at my own violence, I was shooting at the violence of the era," she stated about the process behind her Tirs.

That sense of rawness, of a surface being pierced, or torn and peeled away to reveal the colors beneath, has long resonated beyond art, finding its way into fashion, particularly in ripped designs.

In 1938, almost as if anticipating the destruction to come, Elsa Schiaparelli, in collaboration with Salvador Dalí, created an evening gown that transformed this concept into surreal couture. The dress featured a trompe-l'oeil print of jagged, torn fabric, with a black "tongue" seemingly peeling back to reveal a layer of pink underneath.

Originally crafted in pale blue silk crêpe (now faded to an off-white) the gown was accompanied by a flowing veil and striking pink gloves designed to mimic exposed flesh. A surreal paradox emerged: the gloves appeared like skin, yet they protected it. The accompanying headscarf, genuinely torn, unveiled a flash of Schiaparelli's signature shocking pink beneath. Echoing the haunting imagery in Dalí's Three Young Surrealist Women (1936), the trompe-l'oeil tears on Schiap's dress evoked flayed skin, both unsettling and undeniably beautiful.

Fashion has continued to revisit this motif, exploring destruction as a form of artistic expression. In a previous post, we examined the theme of torn and shredded designs, mentioning Viktor & Rolf’s Spring/Summer 2024 Haute Couture collection.

More recently, Jason Wu's Autumn/Winter 2025 collection revisited this aesthetic in two dresses one in deep blood red, the other in a delicate nude beige. Like Schiaparelli's high-contrast design, these dresses featured laser-cut details that curled and peeled away from the fabric, revealing the layers underneath. Through them the designer embraced imperfection, a theme he also tackled in the same collection through raw seams and exposed darts turned into decorative elements.

The two "torn" gowns, felt like relics, garments left to decay in an attic, only to be rediscovered and worn again (other designs in this collection reflected this philosophy, or this connection with the past as well; for example, inspired by his own archives, Wu digitally photographed both sides of a flat-laid vintage dress, and then replicated the images into a jacquard fabric).

Beyond their visual appeal, designs with torn elements carry certain symbolisms: usually the tears are not merely wounds, but rips and shreds tell stories of strength and endurance, they are marks of survival, defiance, and evoke the raw poetry of imperfection and the beauty found in flaws.