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The city of Barcelona burned as anarchists rebelled against Franco's Catholic fascist movement. A movement that used the church as a tool of control. One culture, one language, one religion. In Barcelona, the capital of Catalan identity and revolutionary thought, churches had become symbols of everything the Republic was fighting against. One large unfinished basilica imposed itself over Barcelona, designed by the controversial architect, the late Antoni Gaudí, who designed luxurious lodgings for the bourgeoisie of Barcelona. Casa Milà and Casa Batlló, built in the early 1900s, and extravagant by even modern standards.
Sagrada Família, Gaudí's final unfinished project before his untimely death, was a monument to everything the anarchists were fighting against. They smashed in the door of Gaudí's former home and workroom inside the basilica and began systematically destroying the architect's final work, leaving a few precious clues to Gaudí's final vision for his magnum opus. Fragments of plaster molds, sketches of facades, templates marking column cross sections for stonemasons, clues to a puzzle that would take 144 years to solve, with the final pieces slotting in place in June 2026.
Gaudí's vision is finally complete. A task made possible because the network of tree-like supports and complex curved surfaces that Gaudí designed were carved by mathematical equations and physics. Gaudí's obsession with the natural world and desire to celebrate his God's creations led him to design buildings inspired and molded by nature. Columns mimicking trees and skeletons, arches mirroring rib cages and seashell-inspired spiral stairways, spires emulating crystals and ceilings that rival forest canopies for their natural beauty. His gargoyles were not grotesque creatures of imagination, but the beautiful animals that inhabited Barcelona's gardens. Their designs are
all rooted in natural phenomenon, but for a human mind to recreate them in stone, took a man of true genius. Because he based his designs in natural phenomena dictated by the laws of physics, he left a code behind for researchers to uncover. A code that could be decrypted with fragments of the answer, allowing designs to be procedurally regenerated with parameters in a design software originally designed to model the complex curved surfaces of fighter jet wings. How did they do it? How do you finish building something this complex from fragments alone, across generations, without betraying the vision of the man who dreamed of it?
This is the story of Sagrada Familia. Barcelona is a city characterized by regimental city blocks and wide linear streets, a departure from the narrow winding streets of most European cities. Yet, nestled in these rigid streets are some of the most unique and beautiful buildings ever created, each rooted in nature through structural forms and designs. These beautiful structures stand out among their neighbors and are the work of one of the world's greatest architects, Antoni Gaudí. Gaudí was not just a master architect. Designing buildings in creative and innovative ways is the challenge of an artist. He was also a master engineer.
He understood how these shapes impacted the structural integrity of the building and allowed physics and nature to dictate his designs. Rather than fight against the laws of nature, he worked with them. He bridged art and science like no man before. He understood that nature is defined by the laws of mathematics, and to him, this was the ultimate celebration of God. So, how did Antoni Gaudí design something so complex in an era when computational analysis did not exist? Evolution happened upon these complicated structures through trial and error. Natural arches are the work of chance. The weak simply fall before we can witness them. While plants develop cells capable of sensing the direction of gravity to
influence their growth patterns, bone cells are stimulated to grow and multiply when placed under stress. To Gaudi, these governing laws of nature were God's laws, and God's house should follow these rules. The challenge that Gaudi faced was one of material strengths. His primary building material came from the nearby quarry. It was Montjuic stone, a type of sandstone. Like all stones, it is strongest in compression. Place a rock in compression and it can withstand enormous pressure, but place it in tension and tiny imperfections in the rock allow cracks to grow, and soon the entire stone will fracture along those cracks. The challenge with constructing structures with stone is primarily one of keeping
the stone in compression at all times. This has been a well-known building technique for thousands of years, but it was the Romans who truly saw and utilized its potential. Unlike Greek structures characterized by vertical posts and horizontal lintel constructions, Roman buildings are defined by arches and domes, curves designed to follow an imaginary path of force, keeping each stone in its construction in compression. They raised massive structures like their famous aqueducts and Pantheon dome, structures that still stand today, a testament to their sturdiness. This imaginary path is called the line of thrust, and imagining it was Gaudi's specialty. Designing with these concepts in mind is relatively simple for a 2D
structure like a aqueduct, but expanding it out to form something as complex as the Sagrada Familia adds a whole other dimension of complexity. Even these simple columns of the Basilica's interior split and diverge like growing trees. The arches of the Passion facade sweep outwards and defy belief that they could possibly remain standing when they're constructed from nothing more than sandstone. So, how did Gaudi do it? Simple. He used strings. Flexible strings can only hang in pure tension. Hang a rope from a single point and it will hang directly downwards, the entire length of the string in tension. Hang it between two points and it will sag
downwards until once again the entire string is in tension. Add more weight and it will sag with a deeper parabolic arch to allow it to remain in tension. You can see a pattern developing here. We can use strings to map out those lines of thrust. Gaudi hung a 1 to 10 scale floor plan in the air and began attaching strings to anchor points where the columns would stand and started hanging weights. Each weight was scaled to represent roughly 1/10,000 of the load the real column would have to bear and they were placed on nodes where the columns met new thrust vectors. This method existed before Gaudi but Gaudi took it to another level to design intricate and sometimes seemingly unstable designs.
It's most clearly seen in the strange Guell Crypt. A building devoid of historical style influence, its leaning columns, odd angles, and lack of symmetry was a study in this analytical approach. Gaudi sometimes hung cloth over these models to resolve their design to his eye or would take a photograph and draw over them. Contrary to what many articles say online or whatever AI decides to hallucinate, the string model you see in the Sagrada Familia museum, clearly labeled, is not from the Sagrada Familia. It is from the Guell Crypt. Gaudi used the crypt as a stepping stone. By the time he was designing the Sagrada Familia, he didn't need strings anymore. He calculated the weight of the vaults, found the center
of forces of each section, and drew the arch directly from the column base to that point. When he talked about this jump, he said that the two methods were the same but that one was born out of the other. In 1914, at the age of 62, Gaudi moved to the unfinished church. His final years would be dedicated to the Sagrada Familia masterpiece. His obsession with his final work took over his life. He neglected his personal appearance and became a disheveled recluse. His days were devoted to praying and overseeing the design and construction of the Sagrada Familia. He stopped producing conventional drawings and devoted himself to building three-dimensional plaster models, not flat plans that required interpretation.
These were intended to be the ultimate guide for future generations to follow. But on June 7th, 1926, disaster struck. At the age of 73, Gaudí was struck by a tram on his daily walk to confession and was left to die in the streets. Passersby did not recognize the ragged man as the famous and beloved architect. Mistaking him for a homeless man, he was left to die in the streets. Hours later, Gaudí was taken to the hospital but received only basic care. When he was finally recognized, it was too late. No more could be done to save his life, and he died 2 days later on June 10th, 1926.
The funeral that followed shut down Barcelona streets. The residents of Barcelona showed up en masse, marching his coffin to its final resting place in the crypt of the Sagrada Familia. With the mastermind behind the complex project gone, completing it became a Herculean task, made even more difficult by the outbreak of the Spanish Civil War in 1936. A secular republic at war with Franco's Catholic fascist movement that used the church as a tool of control. In the summer of 1936, anarchist groups ransacked every church in the city, including one large unfinished basilica.
Its imposing structure was a monument to everything they were fighting against. Inside, they destroyed the carefully crafted plaster molds that Gaudí created over the past decade of solitude. An already difficult task just became the world's most difficult puzzle. Construction of the Sagrada Familia could have ceased here. Instead, this event began a nearly century-long project to reverse engineer Gaudi's genius. The next two decades were devoted to slowly cataloging all the broken pieces, sketches, and clues to Gaudi's vision. Decades flew by as the detective work continued, and this brought with it another problem. The once plentiful
supply of stone from the Montjuïc quarry was running dry. Montjuïc, literally meaning Jewish mountain in Catalan, is located right next to the old city of Barcelona. A strategic high point beside the Llobregat river and the Mediterranean. It's been an attractive place to call home for settlers and conquerors throughout human history, but the mountain's appearance began to change in Barcelona's Roman era when the mountain became the growing city's primary source of stone and a valuable export to the empire. This sandstone gives the Sagrada Familia its distinctive tan color, and from afar it gives the basilica the appearance of a giant termite mound that somehow burst out of the very ground it
was built upon. But up close, you can see the beautiful variations in the individual stones quarried from Barcelona's heart. The dusty browns, charcoal grays, tanned orange, and even hints of purple are most noticeable in the spires of the Nativity facade. Constructed from smaller bricks of Montjuïc stone, a symptom of the dwindling supply of large quarry blocks that has only added to the story and beauty of the building. But the sandstone wasn't just beautiful. Its high quartz content makes it more durable than most sedimentary rocks, making it a valuable building resource found in historic buildings all over Barcelona. The Basilica of Santa Maria del Mar, the Barcelona Cathedral,
Castell de Montjuïc, a fortress on the mountain itself, and the Roman Temple of Augustus. But it's its use in everyday buildings throughout Barcelona that makes the stone an everyday sight for every resident of Barcelona, and led to its eventual scarcity. You can even see Hebrew writing scattered on walls around the city, remnants of ancient Jewish gravestones taken from the mountain. High-quality stone was getting harder to find, leading to intensifying mining activity with the growing metropolis just below us. And in 1957, Montjuïc was made a protected city park for the people of Barcelona. With no suitable replacement for the stone, the sculptors' hands soon became idle. The stone's availability was limited to
whatever was left over in stocks or what could be scavenged from other buildings in Catalonia. A lifeline was found during the remodeling and excavation of the old Olympic stadium in preparation for the 1992 Summer Olympics. Located in the center of the protected city park, 1,000 cubic meters of Montjuïc stone was excavated during the lowering of its plain field to allow the expansion of spectator capacity. This stone allowed construction of the Passion facade. The imposing facade is supported by six skeletal angled columns, requiring the highest quality silicated sandstone.
These rib-like structures face west, facing the setting sun, casting long shadows across the facade's hooded wall. Light and shadow bring life to the carvings depicting the torment of Jesus' crucifixion. The design of this facade was recreated from sketches Gaudí drew himself while gravely ill visiting mountain retreat in the Pyrenees, escaping the poor air of the increasingly industrialized city. We know Gaudí was contemplating his own mortality during this trip as he also wrote his will. He explicitly wished for the design to be harsh and cruel as if it was made from bones. Sculptor Josep Maria Subirachs took these instructions
and passion from his predecessor to design the sculptures of the Passion facade. So, lived inside the basilica just as Gaudí did, and his design is faithful to Gaudí's original drawings while adding an almost modern brutalist aesthetic. He even left nods to the legacy of Gaudí. These two soldiers' helmets take the shape of Casa Milà's chimneys, completed in 1910, and this character was modeled on Gaudí himself. This facade juxtaposes its opposite facade in the Nativity facing the rising sun in the east, symbolizing life, death, and rebirth.
Subirachs completed his work on the Passion facade in 2005 and passed away in 2014. This building has witnessed the birth and death of its very own creators, and with the passing of time, new technologies arrived that gave new life to architectural clues left behind by Gaudí. Take the columns. Gaudí designed them to feel organic. Soft curves forming edges as they rise, like the canopy of a forest overhead. Gaudí had created zinc templates that marked the cross sections of these columns at 1-m intervals, so stonemasons could cut the stone to smoothly transition from one profile to the next. But, between each interval, there was no real guidance on what Gaudí intended. How Gaudí instructed
stonemasons to carve between templates was never fully resolved. So, architects went back to the drawing board, this time digitally, trying to reconstruct the process. If you look at the bottom of the large main columns inside, you'll see this curved star pattern. It's actually two copies of the same shape counter-rotating as the column rises. Their intersection makes the column. Gaudí did this with many shapes. At the top of the columns, you can see what the counter-rotated rectangles would look like, and none of this could be modeled in conventional architectural software. With each curve of the building governed
by physics, no architectural software at the time could accurately recreate what Gaudi intended. Architecture software of the day utilized something called non-uniform rational B-lines or nerves to connect vertices with a digital skin. The way Gaudi's geometry worked, lines naturally split, emerge from smooth surfaces, or dissolve into them. Conventional architecture software that used nerves had no tools to create these lines. To solve this problem, the architects turned to the aviation industry who had spent the last six decades perfecting shapes governed by strict physical laws. CATIA was developed in 1977 to aid French aircraft manufacturer Dassault to develop their next generation fighter,
the Mirage. Its wings, crafted to manage airflow at both subsonic and supersonic speeds, were too crafted from natural laws. This was a turning point. These new tools unlocked new ways to read the surviving clues, and the timing was perfect as the vaults and windows were beginning to take shape. So, how did they figure out what Gaudi wanted? One window fragment of a scale model had survived. In it, you could see that each pane was surrounded by a smooth surface, but the key was that Gaudi had used a ruled surface, one generated entirely from straight lines. This particular one
was made by twisting a cylinder. The result is that light enters without hard shadows, gliding across the interior, and letting the stained glass do its work. A ruled surface is defined by a set of variables that control its geometry. They scanned the surviving plaster fragment, placed parametric hourglass shapes over each window, and adjusted the variables until the model matched exactly what Gaudi had built. With these variables locked in, the puzzle just got easier, like a Sudoku puzzle revealing itself number by number. From a single fragment, they could reconstruct the design with mathematical precision.
Look up at the vaults, and you will see the same ruled surfaces scaled up using the same parametric method. The great windows of the Sagrada Familia, with their soft edges and vast fields of uninterrupted glass, turned the interior into a wide, empty canvas waiting to be filled with light. Joan Vila-Grau was a Catalan painter and stained glass artist who had spent decades restoring medieval windows across Catalonia, which is precisely why in 1999 the board of construction chose him for the commission. Gaudí had oriented the church with the Nativity facade facing east and the Passion facade facing west, birth on one side and death on the other. Vila-Grau took that logic and painted with it, giving the east cool blues and
aquamarines and the west warm reds and ambers so that the mood of the whole interior shifts with the sun. He never thought in individual windows, but in one painting. Each design began as a watercolor, the colors flowing naturally across the paper. And when the glass was cut, the lead lines followed the natural divisions the painting had already made. That watercolor was then scaled up and translated into glass piece by piece, each panel part of the same vast composition. The windows were a perfect test case for the new aviation design software, and the method they developed could even help reconstruct designs with no surviving models at all.
The sole surviving evidence of the Passion facade was a single photograph of a sketch. From that, a plaster model had been built in the early documentation years. Architects scanned it and brought it into the digital model, but something was off. When they overlaid the scan with the sketch, the rib-like columns didn't line up. A new puzzle to solve. Gaudí imagined the upper facade as a kind of rib cage, columns leaning inward and growing taller as they reached the center, each one flaring out at the top and bottom.
The columns used the same twisted cylinder found throughout the church, but paired with a second ruled surface, one formed by twisting two lines. That surface met the cylinder at the column's foot. Both shapes were parametric, both defined by variables. The question was, which values Gaudi had used? They found them from one photograph of a sketch drawn nearly a century earlier. They reconstructed the facade exactly as Gaudi had imagined using the same geometric language he used throughout the church.
Gaudi's work was always defined by natural laws, and rather than simply attempting to trace his designs, the architects wished to find a way to recreate them with the same mathematical constants that influenced the growth of petals on a flower. A celebration of nature, life, and humans' ability to observe and understand it. A cathedral to God's creations, something that transcends any scripture and connects all religions. Software unlocked the final pieces of Gaudi's puzzle, but there were many more modern technologies that have helped us magnum opus. Computer-controlled machining has allowed the digitized models to come to life faster than ever
before and ensure perfect fits between the pieces and the internal steel supports. Because in the final years of construction, the workers were not assembling the tower stone by stone like in Gaudi's time. They were using tension steel bars running through the center of the stones to compress the stones together and form a larger panel, allowing pieces to be partially assembled before being lifted to the tower and assembled like a giant stone Lego set. Cash flow has increased drastically over the years, too. For decades, the only money the Sagrada Familia received was through donations to the church. In the early days of construction, these donations came in
dribs and drabs, but today the church has no shortage of funding, being one of the most popular tourist sites in the world. Since it opened its doors to the public, Sagrada Familia has raising a consistent and reliable cash flow from the millions of tourists that pay to visit it every year, paying for it the materials and workers needed to complete it. In June 2026, the cross was placed on the tower of Jesus Christ, making the Sagrada Familia, at 172 m, the tallest church in the world, marking the completion of the main build after 144 years. But, the story isn't over. When Gaudí designed the church, it sat among open fields. The city grew far faster than the building could rise. The main entrance door now sits 10 m
above street level, and where sheep once grazed, there are dense Catalan neighborhoods. The completion of the Sagrada Familia is no longer a technical challenge. It is a legal and moral one. Gaudí's original plans called for a grand avenue leading up to the church, but that land was built over in the 1970s and Barcelona expanded. Planning permission for the final design sits in legal limbo, with major ethical questions to be answered. Barcelona, like many cities, is facing a housing crisis. Demolishing homes to finish a church in one of the densest cities in Europe, or making room for open green spaces in an overcrowded city. For now, we can all enjoy the beauty
created by a devout genius who wanted to celebrate the holiness of life and all that comes with it, birth, death, and the in-between. This video wasn't really designed for the algorithm. It's a passion project for a building that I adore, and as part of that, I sent Josie, my co-writer on this video, to visit Joan Vila Grau, the man behind Sagrada Familia's beautiful stained glass windows. He recorded the excellent footage that you saw during that segment and conducted an interview as part of the research process, entirely in Catalan, and we've uploaded that to Nebula as a bonus video with
subtitles, something we can only afford because of our viewers' support. But, there is way more bonus content up on Nebula that you can watch right now. Our Anatomy of series uses industrial CT scans to peer inside fascinating devices. And, so many of you signed up to Nebula to watch that show that it's been greenlit for a new season with a higher budget. Your support of Nebula helps fund this channel, especially as AI and VC-backed channels flood YouTube and make it harder and harder to compete as an independent channel. We've seen our views collapse since YouTube has pivoted to shorts and AI, and are really struggling to turn things around. If you value real scientific journalism without the biases and
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