Phyllotaxis
The elegant mathematics of spiral arrangements in nature. Discover how plants optimize growth through Fibonacci sequences and the golden angle, creating patterns of extraordinary beauty and efficiency.
What you'll find here
Simulation
An interactive tool to explore how different angles and parameters create various spiral patterns found in nature.
History
The fascinating story of how scientists and mathematicians unraveled the mysteries of plant spiral patterns over centuries.
Theory
Understanding the golden angle, Fibonacci numbers, and why these patterns emerge so consistently in the plant kingdom.
Why it matters
Optimal packing: Phyllotaxis allows plants to maximize exposure to sunlight and rain while minimizing overlap between leaves, seeds, or petals.
Universal patterns: The same mathematical principles appear across vastly different species, from tiny succulents to towering sunflowers.
Biomimicry inspiration: Understanding these natural algorithms helps engineers design more efficient solar panels, antennas, and architectural structures.
Examples in nature
Phyllotaxis patterns can be observed throughout the plant kingdom, from flower heads to leaf arrangements.
Sunflower
Seeds arranged in Fibonacci spirals
Pine Cone
Scales following golden angle
Succulent
Leaves in perfect rosette
Aloe
Spiral leaf arrangement
Artichoke
Bracts in phyllotactic pattern
Cactus
Areoles in spiral rows
Begin your exploration
Dive into the theory behind these remarkable patterns, or explore the historical journey of their discovery.