The Fibonacci Sequence, the Golden Ratio, and the Art of Pattern

The Golden Ratio

What do math, specifically the Fibonacci sequence, and art have in common? Hint: the golden ratio!

In the world of art and design, math quietly plays a starring role. The Fibonacci sequence—1, 1, 2, 3, 5, 8, 13, and so on—builds from the simple idea that each number is the sum of the two before it. From this elegant progression comes the golden ratio, often expressed as approximately 1.618. The golden ratio is presented as a specific proportional relationship: when a line (or rectangle) is divided so that the whole relates to the larger part in the same way the larger part relates to the smaller part. When translated into form or proportion, it creates balance and visual harmony that feels naturally pleasing. This balance appears everywhere from the spirals of sunflowers to the geometry of seashells, which is why artists and designers have leaned on it for centuries to create compositions that feel effortlessly “right” to the human eye.

In art and print design, the golden ratio guides how shapes and layouts flow. Renaissance painters like Leonardo da Vinci and architects such as Le Corbusier relied on its proportions to structure their work (Hemenway, 2005). In modern design, it influences how we arrange images, text, and patterns—giving each element room to breathe without feeling too rigid or too random. The result is a sense of rhythm that draws the viewer in. Even in digital media and print, designers use golden rectangles or Fibonacci spirals to decide spacing and scale.

A central point is that some artists (for example, Renaissance and modern painters fascinated by geometry) have consciously used golden rectangles, grids, or pentagonal structures in their compositions. Livio discusses such examples to show how phi can organize space, create balance, and guide the viewer’s eye, especially through rectangles and spiral-like flows. At the same time, he stresses that many famous works only loosely fit golden-ratio overlays and that compositional strength comes from a combination of proportion, rhythm, and narrative, not a single number.​

When it comes to colour and pattern, the same principles apply. The golden ratio can help balance strong shades with subtler tones, ensuring a palette feels both dynamic and cohesive. Patterns that mirror Fibonacci-inspired spirals or proportions often appear more organic, echoing the patterns found in nature—petals, pinecones, or waves. These natural rhythms make interiors feel calming and familiar, while still offering refinement. Designers often reference these proportions, whether consciously or intuitively, when developing colour harmonies and repeat patterns for textiles or wallpaper.

That connection between math and beauty is what gives pattern design its enduring appeal. Many of the most captivating wallpapers are built on principles that trace back to Fibonacci. The repetition, order, and flow that come from those patterns make a room feel inviting and alive. When you choose wallpaper designed with these timeless proportions in mind, you are not just selecting a print—you are inviting centuries of artistic wisdom into your home. Explore our collection at Papered Walls to find designs that bring this natural harmony to your own space.

References

Livio, M. (2002). The Golden Ratio: The Story of Phi, the World’s Most Astonishing Number. Broadway Books.Hemenway, P. (2005). Divine Proportion: Phi In Art, Nature, and Science. Sterling Publishing.