{"title":"Signature","description":"\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003eThe Signature series forms the core of Axisophy - a growing body of mathematical visualisations and scientific infographics that reveal the structures underlying our world.\u003c\/p\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003eThe range spans number theory, geometry, evolutionary biology, astronomy, and earth science. You'll find prime number patterns made visible in the Ulam and Sacks spirals, recursive fractal constructions like the Apollonian gasket, radial phylogenetic trees mapping the evolutionary relationships of hundreds of species, and data-rich infographics charting geological time and planetary systems.\u003c\/p\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003eEach design begins with research - published datasets, peer-reviewed science, established mathematical theory - and translates it into clean, considered visual form. The emphasis is on clarity and proportion: designs that work as information and as objects on the wall.\u003c\/p\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003ePrinted on 250gsm archival matte paper through our global print network, the Signature series offers museum-quality printing with worldwide delivery. These are the prints that started Axisophy - and the foundation everything else builds from.\u003c\/p\u003e","products":[{"product_id":"ulam-spiral-minimal","title":"Ulam Spiral","description":"\u003cp\u003eThis Ulam spiral art print turns one of mathematics’ most striking visual patterns into a design-led work for the wall. More than 22,000 prime numbers are revealed within Stanislaw Ulam’s celebrated square spiral, creating an image that feels at once orderly, surprising and quietly hypnotic.\u003c\/p\u003e\n\u003cp\u003eThe print maps every number from 1 to 251,001 across a 501 × 501 grid, with 22,115 prime numbers highlighted within the spiral. Features such as twin-prime pairs and shifting prime gaps hint at the strange balance of rhythm and irregularity hidden in the number system.\u003c\/p\u003e\n\u003cp\u003eThe Ulam spiral is named after the mathematician Stanislaw Ulam, who discovered its unexpected prime-number patterns while sketching numbers in a spiral. His observation revealed clustering and alignments that are difficult to see in an ordinary list, opening up a new way of understanding number through image.\u003c\/p\u003e\n\u003cp\u003eSeen this way, the primes become less like an abstract sequence and more like a landscape - a field of recurring structures, gaps and surprises. The result is an image that rewards both close study and everyday living, making it especially suited to studies, offices, libraries and other thoughtful interiors.\u003c\/p\u003e","brand":"Axisophy","offers":[{"title":"Large (50 × 70 cm | 20 × 28 in)","offer_id":45864092532897,"sku":"APW-USM-P-500x700-AM-WHT","price":50.0,"currency_code":"GBP","in_stock":true},{"title":"XLarge (70 × 100 cm | 28 × 40 in)","offer_id":45864092565665,"sku":"APW-USM-P-700x1000-AM-WHT","price":80.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0483\/1546\/5889\/files\/Axisophy-ulam-spiral-white-print.jpg?v=1762261536"},{"product_id":"sacks-spiral-minimal","title":"Sacks Spiral – Minimal","description":"\u003cp\u003eThe Sacks Spiral offers a striking visualisation of prime numbers mapped through an innovative spiral geometry. This print arranges the numbers from 1 to 250,000 using the Sacks spiral method, where each point is placed according to polar coordinates determined by Sacks' formula. The result is a sweeping, organic spiral in which prime numbers - 22,044 out of 250,000 plotted (8.82%) - stand out as luminous markers amid subtle arcs and clusters.\u003c\/p\u003e\n\u003cp\u003eThis elegant mapping was introduced by mathematician Robert Sacks, whose unique approach showcased mathematical beauty by transforming the classic number line into a spiral with meaningful spatial relationships. The distinctive arrangement highlights 2,588 twin-prime pairs, the largest prime gap of 86, and invites exploration of both structure and randomness in prime distribution. Each coordinate places the primes in positions where underlying patterns become visible.\u003c\/p\u003e\n\u003cp\u003eSuch visualisations reveal new complexity in the “periodic table of numbers” - making tangible the intricate and sometimes hidden relationships among primes. Sacks spirals unlock symmetries and clustering that are not always apparent from list-based representations, furthering mathematical and artistic curiosity for viewers and researchers alike.\u003c\/p\u003e\n\u003cp\u003eThis open edition print is rendered in minimalist black on white, using 250gsm archival matte paper for an exceptionally smooth surface and lasting quality. The deep black ink and fine-grained finish ensure every detail is captured with clarity and richness, providing a museum-ready foundation for mathematical art and discovery.\u003c\/p\u003e","brand":"Axisophy","offers":[{"title":"Large (50 × 70 cm | 20 × 28 in)","offer_id":45864092467361,"sku":"APW-SSM-P-500x700-AM-WHT","price":80.0,"currency_code":"GBP","in_stock":true},{"title":"XLarge (70 × 100 cm | 28 × 40 in)","offer_id":45864092500129,"sku":"APW-SSM-P-700x1000-AM-WHT","price":125.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0483\/1546\/5889\/files\/Axisophy-sacks-spiral-white-print.jpg?v=1762261420"},{"product_id":"deepest-trenches","title":"Deepest Trenches","description":"\u003cp\u003eThe companion to \u003ci\u003eThe Highest Mountains\u003c\/i\u003e, this print inverts the perspective to show the ocean’s profound depths. Each trench is scaled by depth, from the Peru-Chile Trench to the Mariana Trench, revealing the extreme yet ordered geometry of the seafloor. The composition mirrors its mountain counterpart, turning measurement into form — a calm, graphic descent into Earth’s hidden architecture.\u003c\/p\u003e","brand":"Axisophy","offers":[{"title":"Large (50 × 70 cm | 20 × 28 in)","offer_id":45864092401825,"sku":"APW-DTR-P-500x700-AM-WHT","price":50.0,"currency_code":"GBP","in_stock":true},{"title":"XLarge (70 × 100 cm | 28 × 40 in)","offer_id":45864092434593,"sku":"APW-DTR-P-700x1000-AM-WHT","price":80.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0483\/1546\/5889\/files\/Axisophy-deepest-trenches-white-print.jpg?v=1762261317"},{"product_id":"highest-mountains","title":"Highest Mountains","description":"\u003cp\u003eA graphic study of Earth’s great summits, arranged by elevation. From Annapurna I to Mount Everest, each peak is depicted as part of a continuous geometric range, emphasising the narrow band in which all eight-thousanders exist. The result is both an infographic and a minimalist landscape — a precise visual comparison of the planet’s highest points.\u003c\/p\u003e","brand":"Axisophy","offers":[{"title":"Large (50 × 70 cm | 20 × 28 in)","offer_id":45864092336289,"sku":"APW-GEO-HMT-P-500x700-AM-COL","price":50.0,"currency_code":"GBP","in_stock":true},{"title":"XLarge (70 × 100 cm | 28 × 40 in)","offer_id":45864092369057,"sku":"APW-GEO-HMT-P-700x1000-AM-COL","price":80.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0483\/1546\/5889\/files\/Axisophy-highest-mountains-white-print.jpg?v=1762261247"},{"product_id":"apollonian-gasket","title":"Apollonian Gasket","description":"\u003cp\u003eThis Apollonian Gasket print presents a classic fractal geometry in striking, precise form. This print begins with a configuration of four starting circles, defined by the root quadruple curvatures: negative twelve, twenty-five, twenty-five, and twenty-eight. Through seven intricate rounds of replacements, new circles are recursively added to fill every possible gap, building up an intricately layered structure.\u003c\/p\u003e\n\u003cp\u003eEach step multiplies the pattern, with circles added in quantities like three, nine, twenty-seven, eighty-one, and eventually over two thousand per depth. The increasing totals quickly soar, culminating in thousands of finely nested shapes.\u003c\/p\u003e\n\u003cp\u003eThis geometric marvel is rooted in mathematical history and named after Apollonius of Perga, who first studied problems related to tangent circles in ancient Greece. The Apollonian gasket exemplifies how simple rules — here, the replacement of gaps with smaller, tangent circles — can yield endlessly complex, self-similar forms. Its one-axis mirror symmetry (classified as D₁) and a universal Hausdorff dimension of roughly 1.30568 make it a showcase for both symmetry and fractal dimension in mathematics.\u003c\/p\u003e\n\u003cp\u003eThe recursive process not only reveals the interplay of geometry and number, but also connects to deeper questions about packing, symmetry, and the distribution of curvatures. Each layer exposes a greater depth and an unexpected richness — visual proof of how mathematical abstraction finds order within limitless complexity.\u003c\/p\u003e\n\u003cp\u003eEvery print is produced in open edition on museum-grade 250gsm archival matte paper, lending both weight and subtlety to the fine detail. Crisp contrasts and a soft matte finish highlight the minute geometry, resulting in a timeless and contemplative addition to any collection or space.\u003c\/p\u003e","brand":"Axisophy","offers":[{"title":"Large (50 × 70 cm | 20 × 28 in)","offer_id":45864092270753,"sku":"APW-AG1-P-500x700-AM-WHT","price":50.0,"currency_code":"GBP","in_stock":true},{"title":"XLarge (70 × 100 cm | 28 × 40 in)","offer_id":45864092303521,"sku":"APW-AG1-P-700x1000-AM-WHT","price":80.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0483\/1546\/5889\/files\/Axisophy-apollonian-gasket-white-print.jpg?v=1762261137"},{"product_id":"fermats-spiral","title":"Fermat’s Spiral","description":"\u003cp\u003eFermat’s Spiral — featured in our Signature collection — transforms a simple mathematical principle into a composition of balance, growth, and natural symmetry. This print traces two intertwined spiral branches, each winding around the centre in perfect opposition and completing twenty full rotations. The construction ensures every turn is spaced evenly, evoking forms seen in nature from sunflower heads to galaxy arms.\u003c\/p\u003e\n\u003cp\u003eMathematically, the distance from the centre increases in direct proportion to the angle swept around — resulting in a spiral where each arm unwraps at a constant rate. One branch is plotted forwards, starting at zero degrees, while the other is mirrored across the centre by beginning at one hundred eighty degrees. Both are scaled so their tightly woven arcs meet a fixed outer radius. Coordinates for the spiral branches are found by multiplying the scaling factor, the square root of the swept angle, and then using both the cosine and sine of that angle to assign every point’s horizontal and vertical placement.\u003c\/p\u003e\n\u003cp\u003eThe remarkable aspect of Fermat’s spiral is how it encodes optimal packing and distribution. In botany, similar spirals allow seeds or leaves to fill space efficiently, while in mathematics, the same pattern surfaces in areas from polar graphing to visualisations of irrational numbers. The layout ensures no two points overlap — demonstrating an arrangement that is as logical as it is aesthetically pleasing.\u003c\/p\u003e\n\u003cp\u003eEach museum-quality print is rendered in crisp detail on 250gsm archival matte paper. The smooth, durable finish beautifully complements the sweeping, precise lines of the spiral, offering a timeless and contemplative celebration of mathematical artistry.\u003c\/p\u003e","brand":"Axisophy","offers":[{"title":"Large (50 × 70 cm | 20 × 28 in)","offer_id":45864092205217,"sku":"APW-FS1-P-500x700-AM-WHT","price":50.0,"currency_code":"GBP","in_stock":true},{"title":"XLarge (70 × 100 cm | 28 × 40 in)","offer_id":45864092237985,"sku":"APW-FS1-P-700x1000-AM-WHT","price":80.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0483\/1546\/5889\/files\/Axisophy-fermats-spiral-white-print.jpg?v=1762261063"},{"product_id":"morse-code","title":"Morse Code","description":"\u003cp\u003eOur Morse Code print pays homage to one of the foundational encoding systems of modern communication. This print features the internationally recognised core set of Morse code as formalised by the ITU Radiocommunication Sector.\u003c\/p\u003e\n\u003cp\u003eDeveloped originally by Samuel Morse and Alfred Vail in 1836, Morse code remains a universal standard for encoding the alphabet and numbers 0 through 9. In this edition, only the essential operational set is presented — no punctuation, special symbols, or accented characters, just the basic code as it is used for tone bursts, flashes of light, or radio signals.\u003c\/p\u003e\n\u003cp\u003eWhat makes Morse code mathematically interesting is its strict system of intervals and timing. A dot has a duration of one time unit; a dash lasts for three. Gaps between symbols, between letters, and between words follow a fixed proportional system, allowing precise manual or machine decoding. These modular timings reflect deep principles of information theory — minimising ambiguity while maximising universal readability. \u003c\/p\u003e\n\u003cp\u003eLike a visual language, the arrangement of dots and dashes creates a rhythm that is both instantly recognisable and quietly poetic. Each letter and number becomes a graphic gesture, linking past innovations in telegraphy to contemporary design. The modality-neutral nature of Morse code means it bridges forms — audible, visible, or tactile — making it truly timeless.\u003c\/p\u003e\n\u003cp\u003eThis open edition print is beautifully rendered in black on white on premium 250gsm archival matte paper. The bold, minimalist composition and crisp paper stock combine for clarity, elegance, and lasting archival quality — perfect for collectors and those who appreciate the art of systems and communication.\u003c\/p\u003e","brand":"Axisophy","offers":[{"title":"Large (50 × 70 cm | 20 × 28 in)","offer_id":45864092172449,"sku":"APW-MSC-P-500x700-AM-COL","price":50.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0483\/1546\/5889\/files\/Axisophy-morse-code-print.jpg?v=1762260952"},{"product_id":"insecta-phylogenetic-tree-500-mono","title":"Insecta Phylogenetic Tree - 500 - Mono","description":"\u003cp\u003eThis phylogenetic tree maps the evolutionary relationships of 500 insect species - from beetles to butterflies, ants to dragonflies - arranged in a radial diagram that reveals the deep structure of the most diverse class of animals on Earth. Insects account for over half of all known living species, and this print captures that extraordinary variety.\u003c\/p\u003e\n\u003cp\u003eThe print draws on current molecular phylogenetics, presenting complex scientific data in a form that rewards both close examination and distant appreciation. See how the major insect orders relate to each other, discover unexpected connections, and appreciate the 400-million-year evolutionary history of these remarkable creatures.\u003c\/p\u003e\n\u003cp\u003e Perfect for entomologists, biology educators, or anyone fascinated by the extraordinary diversity of insect life.\u003c\/p\u003e","brand":"Axisophy","offers":[{"title":"Large (50 × 70 cm | 20 × 28 in)","offer_id":45864090566817,"sku":"AXS-IPT-MONO-500-P-500x700-AM-WHT","price":50.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0483\/1546\/5889\/files\/Axisophy-Insecta-Mono-PhylogeneticTree-print.jpg?v=1762262848"},{"product_id":"dinosauria-phylogenetic-tree-500-mono","title":"Dinosauria Phylogenetic Tree - 500 - Mono","description":"\u003cp\u003eThis phylogenetic tree maps the evolutionary relationships of 500 dinosaur species - from the towering sauropods to the feathered theropods that gave rise to modern birds. Arranged in a radial diagram, it reveals the deep structure of dinosaurian diversity across 165 million years of the Mesozoic Era.\u003c\/p\u003e\n\u003cp\u003eThe print draws on current palaeontological research, presenting complex scientific data in a form that rewards both close examination and distant appreciation. Trace the relationships between T. rex and Velociraptor, see where Triceratops sits among the ornithischians, discover how bird-like some dinosaurs had already become.\u003c\/p\u003e\n\u003cp\u003e Perfect for palaeontology enthusiasts, natural history museums, science educators, or anyone captivated by the age of dinosaurs.\u003c\/p\u003e","brand":"Axisophy","offers":[{"title":"Large (50 × 70 cm | 20 × 28 in)","offer_id":45864090534049,"sku":"AXS-DPT-MONO-500-P-500x700-AM-WHT","price":50.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0483\/1546\/5889\/files\/Axisophy-Dinosauria-Mono-PhylogeneticTree-mockup-1-flat-crop.jpg?v=1762263100"},{"product_id":"mammalia-phylogenetic-tree-500-mono","title":"Mammalia Phylogenetic Tree - 500 - Mono","description":"\u003cp\u003eThis phylogenetic tree maps the evolutionary relationships of 500 mammal species - from whales to bats, elephants to shrews - arranged in a radial diagram that reveals the deep structure of mammalian diversity. Each branch represents millions of years of evolution, showing how the extraordinary range of mammal forms descends from common ancestors.\u003c\/p\u003e\n\u003cp\u003eThe print draws on current molecular phylogenetics, presenting complex scientific data in a form that rewards both close examination and distant appreciation. Trace the connections between primates and rodents, discover how closely related dolphins are to hippos, see the full sweep of our own class of animals.\u003c\/p\u003e\n\u003cp\u003e Perfect for biology educators, natural history enthusiasts, or anyone fascinated by the diversity of life.\u003c\/p\u003e","brand":"Axisophy","offers":[{"title":"Large (50 × 70 cm | 20 × 28 in)","offer_id":45864090435745,"sku":"AXS-MPT-MONO-500-P-500x700-AM-WHT","price":50.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0483\/1546\/5889\/files\/Axisophy-Mammalia-Mono-PhylogeneticTree-print.jpg?v=1762263306"},{"product_id":"aves-phylogenetic-tree-500-mono","title":"Aves Phylogenetic Tree - 500 - Mono","description":"\u003cp\u003eThis phylogenetic tree maps the evolutionary relationships of 500 bird species - from hummingbirds to ostriches, penguins to parrots - arranged in a radial diagram that reveals the deep structure of avian diversity. Each branch represents millions of years of evolution, each species a unique endpoint in an ancient story.\u003c\/p\u003e\n\u003cp\u003eThe print draws on current molecular phylogenetics, presenting complex scientific data in a form that rewards both close examination and distant appreciation. At arm's length, you see the sweep of bird evolution; up close, you can trace the relationships between familiar species and discover unexpected connections.\u003c\/p\u003e\n\u003cp\u003e Perfect for ornithologists, biology educators, birdwatchers, or anyone fascinated by the diversity of life.\u003c\/p\u003e","brand":"Axisophy","offers":[{"title":"Large (50 × 70 cm | 20 × 28 in)","offer_id":45864090304673,"sku":"AXS-APT-MONO-500-P-500x700-AM-WHT","price":50.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0483\/1546\/5889\/files\/Axisophy-Aves-Mono-PhylogeneticTree-print.jpg?v=1762263467"},{"product_id":"geological-timescale-recursive","title":"Geological Timescale - Recursive","description":"\u003cp\u003eThis recursive infographic presents the full sweep of Earth's 4.5 billion year history - from the formation of the planet through the emergence of life, the age of dinosaurs, and the rise of mammals. The stacked, recursive scale system reveals both the immense stretches of deep time and the relatively recent explosion of complex life.\u003c\/p\u003e\n\u003cp\u003eThe design balances scientific accuracy with visual clarity, making the geological timescale accessible and engaging. See how the Cambrian explosion fits within the broader Phanerozoic, how the age of dinosaurs compares to human history, and how our own era is the merest sliver at the end of an ancient story.\u003c\/p\u003e\n\u003cp\u003e Perfect for geology enthusiasts, earth science educators, natural history museums, or anyone interested in the deep history of our planet.\u003c\/p\u003e","brand":"Axisophy","offers":[{"title":"Large (50 × 70 cm | 20 × 28 in)","offer_id":45864090271905,"sku":"AXS-GTSR-COL-P-500x700-AM-WHT","price":50.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0483\/1546\/5889\/files\/Axisophy-Geological-Timescale-print.jpg?v=1762263652"},{"product_id":"e8-coxeter-projection","title":"E8: Coxeter Projection","description":"\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003eE8 is the largest of the four exceptional root systems - a collection of 240 vectors in 8-dimensional space, arranged with a degree of symmetry that has no parallel in lower dimensions. It appears in string theory, in the classification of simple Lie algebras, and in the construction of the densest possible sphere packing in 8 dimensions. Mathematicians have been studying it for over a century and it continues to surprise them.\u003c\/p\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003eThis print shows E8 projected onto its Coxeter plane - a canonical 2D view that preserves the full 30-fold rotational symmetry of the system. Each of the 240 roots falls into one of 8 concentric rings of 30 points. The 6,720 edges connect nearest-neighbour root pairs, each root touching exactly 56 others. Nothing is approximate or artistic - every position, every connection is mathematically exact.\u003c\/p\u003e","brand":"Axisophy","offers":[{"title":"Large (50 × 70 cm | 20 × 28 in)","offer_id":45891882844321,"sku":"APW-E8C-P-500x700-AM-WHT","price":50.0,"currency_code":"GBP","in_stock":true},{"title":"XLarge (70 × 100 cm | 28 × 40 in)","offer_id":45891882877089,"sku":"APW-E8C-P-700x1000-AM-WHT","price":80.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0483\/1546\/5889\/files\/Axisophy-E8-Coxeter-mockup-1.jpg?v=1775494565"},{"product_id":"e7-coxeter-projection","title":"E7: Coxeter Projection","description":"\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003eE7 is the second-largest of the four exceptional root systems, sitting between E8 and E6 in a family of objects with no straightforward lower-dimensional analogue. It has 126 roots in 7-dimensional space, each one connected to 32 others at the nearest-neighbour distance, giving 2,016 edges in total.\u003c\/p\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003eThe Coxeter plane projection collapses all 7 dimensions into a single plane while preserving the system's 18-fold rotational symmetry. The 126 roots arrange themselves into 7 concentric rings of 18 - a structure that is genuinely visible in the print in a way that E8, with its greater density, makes harder to read. If E8 is the overwhelming one, E7 is the one you can actually study.\u003c\/p\u003e","brand":"Axisophy","offers":[{"title":"Large (50 × 70 cm | 20 × 28 in)","offer_id":45891939729569,"sku":"APW-E7C-P-500x700-AM-WHT","price":50.0,"currency_code":"GBP","in_stock":true},{"title":"XLarge (70 × 100 cm | 28 × 40 in)","offer_id":45891939762337,"sku":"APW-E7C-P-700x1000-AM-WHT","price":80.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0483\/1546\/5889\/files\/Axisophy-E7-Coxeter-mockup-1.jpg?v=1775495758"},{"product_id":"f4-coxeter-projection","title":"F4: Coxeter Projection","description":"\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003eF4 is the most unusual of the four exceptional root systems. Unlike E8, E7, and E6, it is non-simply-laced - meaning its 48 roots come in two distinct lengths, 24 long and 24 short, with a ratio of √2 between them. This asymmetry makes F4 structurally richer than its root count suggests, and gives it a character quite different from the other exceptional systems.\u003c\/p\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003eIn the Coxeter plane projection, the 48 roots arrange into 4 concentric rings of 12, with 12-fold rotational symmetry throughout. All 1,128 possible connections between roots are shown - a choice that makes sense for F4, where the nearest-neighbour edge set alone gives an unusually sparse result owing to the mixed root lengths. The full connectivity reveals the geometry more completely.\u003c\/p\u003e","brand":"Axisophy","offers":[{"title":"Large (50 × 70 cm | 20 × 28 in)","offer_id":45891940188321,"sku":"APW-F4C-P-500x700-AM-WHT","price":50.0,"currency_code":"GBP","in_stock":true},{"title":"XLarge (70 × 100 cm | 28 × 40 in)","offer_id":45891940221089,"sku":"APW-F4C-P-700x1000-AM-WHT","price":80.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0483\/1546\/5889\/files\/AxisophyF4-Coxeter-mockup-1.jpg?v=1775495920"},{"product_id":"conformal-map-cm001","title":"Conformal Map CM001","description":"\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003eA conformal map is a function on the complex plane that distorts shapes while preserving angles. Take a regular square grid, apply the function point by point, and the grid emerges curved, stretched, sometimes folded - but every intersection still crosses at 90°. Riemann's mapping theorem, proved in 1851, showed that any simply connected region in the plane can be conformally mapped to any other. The set of possible transformations is effectively unlimited.\u003c\/p\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003e\u003cmeta charset=\"utf-8\"\u003eCM001 spreads the grid into a six-petalled form with sharply pointed lobes alternating with curved scallops. Six lines of compression radiate from the centre, where dense moiré bands mark the regions of steepest distortion. The petal tips show the function at its most expansive, the original grid stretched outward into the surrounding white space.\u003c\/p\u003e","brand":"Axisophy","offers":[{"title":"Large (70 × 70 cm | 28 × 28 in)","offer_id":46163870023841,"sku":"AXS-CM001-S-700x700-AM-WHT","price":70.0,"currency_code":"GBP","in_stock":true},{"title":"XLarge (100 × 100 cm | 40 × 40 in)","offer_id":46163870056609,"sku":"AXS-CM001-S-1000x1000-AM-WHT","price":120.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0483\/1546\/5889\/files\/Axisophy-ConformalMap-CM001-crop-mockup.jpg?v=1777640195"},{"product_id":"conformal-map-cm002","title":"Conformal Map CM002","description":"\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003eA conformal map is a function on the complex plane that distorts shapes while preserving angles. Take a regular square grid, apply the function point by point, and the grid emerges curved, stretched, sometimes folded - but every intersection still crosses at 90°. Riemann's mapping theorem, proved in 1851, showed that any simply connected region in the plane can be conformally mapped to any other. The set of possible transformations is effectively unlimited.\u003c\/p\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003e\u003cmeta charset=\"utf-8\"\u003eCM002 compresses the grid into a bulging cube-shaped envelope, its top and bottom near-flat, its sides curved outward, its corners softly squared. Eight focal points sit on the faces — four around the equator, four above and below — each surrounded by concentric ring structures where the function maps neighbourhoods of the plane down to a point. The interior is a dense, even weave; the visible structure lives at the faces and edges where compression peaks.\u003c\/p\u003e","brand":"Axisophy","offers":[{"title":"Large (70 × 70 cm | 28 × 28 in)","offer_id":46164133609633,"sku":"AXS-CM002-S-700x700-AM-WHT","price":70.0,"currency_code":"GBP","in_stock":true},{"title":"XLarge (100 × 100 cm | 40 × 40 in)","offer_id":46164133642401,"sku":"AXS-CM002-S-1000x1000-AM-WHT","price":120.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0483\/1546\/5889\/files\/Axisophy-ConformalMap-CM002-crop-mockup.jpg?v=1777640790"},{"product_id":"conformal-map-cm003","title":"Conformal Map CM003","description":"\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003eA conformal map is a function on the complex plane that distorts shapes while preserving angles. Take a regular square grid, apply the function point by point, and the grid emerges curved, stretched, sometimes folded - but every intersection still crosses at 90°. Riemann's mapping theorem, proved in 1851, showed that any simply connected region in the plane can be conformally mapped to any other. The set of possible transformations is effectively unlimited.\u003c\/p\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003e\u003cmeta charset=\"utf-8\"\u003eCM003 takes the form of two pointed ellipses overlapping at right angles, creating a soft four-cornered envelope. The dense central disc is where both ellipses share coverage; the lighter outer regions show where only one ellipse extends. The aggregate texture is unusually flat — a near-uniform grey field — with structure visible mainly at the curved boundaries where the ellipses terminate.\u003c\/p\u003e","brand":"Axisophy","offers":[{"title":"Large (70 × 70 cm | 28 × 28 in)","offer_id":46164757610657,"sku":"AXS-CM003-S-700x700-AM-WHT","price":70.0,"currency_code":"GBP","in_stock":true},{"title":"XLarge (100 × 100 cm | 40 × 40 in)","offer_id":46164757643425,"sku":"AXS-CM003-S-1000x1000-AM-WHT","price":120.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0483\/1546\/5889\/files\/Axisophy-ConformalMap-CM003-crop-mockup.jpg?v=1777641375"},{"product_id":"conformal-map-cm004","title":"Conformal Map CM004","description":"\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003eA conformal map is a function on the complex plane that distorts shapes while preserving angles. Take a regular square grid, apply the function point by point, and the grid emerges curved, stretched, sometimes folded - but every intersection still crosses at 90°. Riemann's mapping theorem, proved in 1851, showed that any simply connected region in the plane can be conformally mapped to any other. The set of possible transformations is effectively unlimited.\u003c\/p\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003e\u003cmeta charset=\"utf-8\"\u003e\u003cmeta charset=\"utf-8\"\u003eCM004 is the most structurally complex print in the series. The grid resolves into a layered system of concentric rings, with additional features extending outward from the main circular form into pointed and curved protrusions. Different regions carry markedly different densities, producing alternating bands of light and dark. The overall composition is fourfold symmetric, but the internal organisation rewards close inspection rather than reducing to a single readable form.\u003cbr\u003e\u003c\/p\u003e","brand":"Axisophy","offers":[{"title":"Large (70 × 70 cm | 28 × 28 in)","offer_id":46164813512865,"sku":"AXS-CM004-S-700x700-AM-WHT","price":70.0,"currency_code":"GBP","in_stock":true},{"title":"XLarge (100 × 100 cm | 40 × 40 in)","offer_id":46164813545633,"sku":"AXS-CM004-S-1000x1000-AM-WHT","price":120.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0483\/1546\/5889\/files\/Axisophy-ConformalMap-CM004-crop-mockup.jpg?v=1777641762"},{"product_id":"conformal-map-cm006","title":"Conformal Map CM006","description":"\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003eA conformal map is a function on the complex plane that distorts shapes while preserving angles. Take a regular square grid, apply the function point by point, and the grid emerges curved, stretched, sometimes folded - but every intersection still crosses at 90°. Riemann's mapping theorem, proved in 1851, showed that any simply connected region in the plane can be conformally mapped to any other. The set of possible transformations is effectively unlimited.\u003c\/p\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003e\u003cmeta charset=\"utf-8\"\u003e\u003cmeta charset=\"utf-8\"\u003eCM006 takes the form of two intersecting lenses, oriented horizontally and vertically, producing a four-cornered envelope with a dense black core at the centre. The compression toward this central singularity is smooth and continuous — the grid darkens from the periphery inward in a tight gradient. At the four corners, the grid thins to its sparsest, lightest weave.\u003cbr\u003e\u003c\/p\u003e","brand":"Axisophy","offers":[{"title":"Large (70 × 70 cm | 28 × 28 in)","offer_id":46164815478945,"sku":"AXS-CM006-S-700x700-AM-WHT","price":70.0,"currency_code":"GBP","in_stock":true},{"title":"XLarge (100 × 100 cm | 40 × 40 in)","offer_id":46164815511713,"sku":"AXS-CM006-S-1000x1000-AM-WHT","price":120.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0483\/1546\/5889\/files\/Axisophy-ConformalMap-CM006-crop-mockup.jpg?v=1777641957"},{"product_id":"conformal-map-cm007","title":"Conformal Map CM007","description":"\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003eA conformal map is a function on the complex plane that distorts shapes while preserving angles. Take a regular square grid, apply the function point by point, and the grid emerges curved, stretched, sometimes folded - but every intersection still crosses at 90°. Riemann's mapping theorem, proved in 1851, showed that any simply connected region in the plane can be conformally mapped to any other. The set of possible transformations is effectively unlimited.\u003c\/p\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003e\u003cmeta charset=\"utf-8\"\u003e\u003cmeta charset=\"utf-8\"\u003eCM007 sits inside a soft square envelope with four small protrusions at the diagonals. The interior carries a ripple pattern of concentric rings — more numerous and more closely spaced than the related CM008 — radiating from a central node. Each ring marks a circular zone where the function changes its rate of compression. The overall texture is smooth, with the rings themselves providing the only sharp edges in the composition.\u003cbr\u003e\u003c\/p\u003e","brand":"Axisophy","offers":[{"title":"Large (70 × 70 cm | 28 × 28 in)","offer_id":46164901298337,"sku":"AXS-CM007-S-700x700-AM-WHT","price":70.0,"currency_code":"GBP","in_stock":true},{"title":"XLarge (100 × 100 cm | 40 × 40 in)","offer_id":46164901331105,"sku":"AXS-CM007-S-1000x1000-AM-WHT","price":120.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0483\/1546\/5889\/files\/Axisophy-ConformalMap-CM007-crop-mockup.jpg?v=1777642148"},{"product_id":"conformal-map-cm008","title":"Conformal Map CM008","description":"\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003eA conformal map is a function on the complex plane that distorts shapes while preserving angles. Take a regular square grid, apply the function point by point, and the grid emerges curved, stretched, sometimes folded - but every intersection still crosses at 90°. Riemann's mapping theorem, proved in 1851, showed that any simply connected region in the plane can be conformally mapped to any other. The set of possible transformations is effectively unlimited.\u003c\/p\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003e\u003cmeta charset=\"utf-8\"\u003e\u003cmeta charset=\"utf-8\"\u003eCM008 is one such transformation, applied to a grid of 500 lines in each direction. The result has a nested circular structure with pinched, concave outer edges - regions where the function compresses the plane heavily, regions where it stretches it thin. The right-angle property holds throughout, even where the grid becomes too dense to resolve individual lines.\u003cbr\u003e\u003c\/p\u003e","brand":"Axisophy","offers":[{"title":"Large (70 × 70 cm | 28 × 28 in)","offer_id":46165062353057,"sku":"AXS-CM008-S-700x700-AM-WHT","price":70.0,"currency_code":"GBP","in_stock":true},{"title":"XLarge (100 × 100 cm | 40 × 40 in)","offer_id":46165062385825,"sku":"AXS-CM008-S-1000x1000-AM-WHT","price":120.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0483\/1546\/5889\/files\/Axisophy-ConformalMap-CM008-crop-mockup.jpg?v=1777642323"},{"product_id":"conformal-map-cm009","title":"Conformal Map CM009","description":"\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003eA conformal map is a function on the complex plane that distorts shapes while preserving angles. Take a regular square grid, apply the function point by point, and the grid emerges curved, stretched, sometimes folded - but every intersection still crosses at 90°. Riemann's mapping theorem, proved in 1851, showed that any simply connected region in the plane can be conformally mapped to any other. The set of possible transformations is effectively unlimited.\u003c\/p\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003e\u003cmeta charset=\"utf-8\"\u003e\u003cmeta charset=\"utf-8\"\u003eCM009 takes the form of a twisted, warped square — its edges curved into cusps, its corners softly rotated out of alignment. Several focal points sit across the interior, each surrounded by tight concentric rings where the function maps neighbourhoods of the plane to single values. The overall surface is a soft, even grey, with the focal points providing the only strong features. The asymmetric placement gives the print a sense of slow rotational drift.\u003cbr\u003e\u003c\/p\u003e","brand":"Axisophy","offers":[{"title":"Large (70 × 70 cm | 28 × 28 in)","offer_id":46165198995617,"sku":"AXS-CM009-S-700x700-AM-WHT","price":70.0,"currency_code":"GBP","in_stock":true},{"title":"XLarge (100 × 100 cm | 40 × 40 in)","offer_id":46165199028385,"sku":"AXS-CM009-S-1000x1000-AM-WHT","price":120.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0483\/1546\/5889\/files\/Axisophy-ConformalMap-CM009-crop-mockup.jpg?v=1777642460"},{"product_id":"ulam-spiral-651","title":"Ulam Spiral 651","description":"\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003eIn 1963, the Polish mathematician Stanisław Ulam sketched numbers in a square spiral during a tedious lecture and noticed something unexpected: the prime numbers tended to fall along diagonal lines. The pattern wasn't a fluke. The Ulam spiral has been studied ever since as one of the strangest visual phenomena in number theory — a hint of structure inside a sequence usually treated as essentially random.\u003c\/p\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003eUlam Spiral 651 maps every integer from 1 to 423,801 across a square grid, with the 35,684 primes marked as black dots. The spiral begins at the centre with 1 and expands outward in the classic right-up-left-down rotation. At this density — roughly 8.4% of the grid is prime — the famous diagonal alignments are less visible as discrete lines and more present as a kind of grain across the surface, with the distribution thinning gradually toward the corners as primes become rarer at higher numbers.\u003c\/p\u003e\n\u003cp class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\"\u003eThe result is a print that reads at two distances. Close up, individual diagonals and clusters reveal themselves. From across the room, the whole image becomes a textured field — a portrait of the primes as a landscape rather than a list.\u003c\/p\u003e","brand":"Axisophy","offers":[{"title":"Large (70 × 70 cm | 28 × 28 in)","offer_id":46165454454945,"sku":"AXS-UL651-S-700x700-AM-WHT","price":70.0,"currency_code":"GBP","in_stock":true},{"title":"XLarge (100 × 100 cm | 40 × 40 in)","offer_id":46165454487713,"sku":"AXS-UL651-S-1000x1000-AM-WHT","price":120.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0483\/1546\/5889\/files\/Axisophy-Ulam-651-crop-mockup.jpg?v=1777642803"}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0483\/1546\/5889\/collections\/apw-signature-collection-1.jpg?v=1762433340","url":"https:\/\/axisophy.com\/collections\/signature.oembed","provider":"Axisophy","version":"1.0","type":"link"}