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.