Patterns,Pattern Application,

& Edge

Courtesy of Bear Kaufmann

Concentric Patterns

Concentric:Growth

Tree Rings

Concentric:Growth Through Accretion

Agate

Too

Hot

Too

Cold

You

Are

Here

Solar System: Not To Scale

Concentric:Radiating & Diffusing Energy

Radial Patterns

Lupine - Lupinus polyphyllus

Spiral Patterns

Medusa’s Head Cactus - Euphorbia caput-medusae

Spirals:For Growth

Tide Pool

Spirals in 3D:Helixes

Chayote Squash - Sechium edule

The SpiralNote that each new square has a side which is as long as the sum of the latest two square's sides.

A M B

• The line AB is divided at point M so that the ratio of the two parts, the smaller MB to the larger AM is the same as the ratio of the larger part AM to the whole AB.

One Way to Understand It

Phi•1.6180339887498948482045868343656381177203091798057628621354486227052604628189044970720720418939113748475408807538689175212663386222353693179318006076672635433389086595939582905638322661319928290267880675208766892501711696207032221043216269548626296313614438149758701220340805887954454749246185695…

Oak Tree - Quercus spp.

Spirals in 3D:Helixes

Argentinian Coast

Spirals:Turbulent Flow

earthobservatory.nasa.gov

Interlocking Spirals:von Karman vortex streets

earthobservatory.nasa.gov

Ideas for Application

Ideas for Application

Ideas for Application

Interlocking Spirals

Spirals in TimeDisturbance

Wave Patterns

Spirals in TimeDisturbance

Wave Patterns

Turbulence

Streamlines

earth.google.com

Alaska

Effects of Flow

Flow

Crenulations

Crenulations:Maximize Edge

Crenulations:Maximize Edge

Crenulations:Habitat

Surface Area to Volume

Bucky

Fractals:fractus = part

Fractals:systems inside systems

patterns within patterns

Measuring Coastline:Mandelbrot, Fractals, and Edge

earth.google.com

“Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning

travel in a straight line.”-Benoît B. Mandelbrot

Edible Fractals

Fractals:Spirals

Edge

The interface between two ecosystems represents a third, more complex,

system which combines both.

Gradients:the rate of transition

Pressure

Temperature

Acidity

Elevation

& other properties

Branches & Networks

Grape Leaf

Branches

Fennel

Leaves and Branching• Leaves are also found in groups of Fibonacci numbers.

• Branching plants always branch off into groups of Fibonacci numbers.

Beech Tree

Branching:Dendritic

Low Diffusion

Low Friction

Higher Diffusion

High Friction

Most Diffusion

For

Least Friction

Branches:For Diffusion and Accumulation

Branches:oldest oaks have 8 orders

Branches:Watersheds and Tributaries

Oakland Hills - Digital Elevation Model

Branches:Water Flow

Jordan earthobservatory.nasa.gov

Networks

earthobservatory.nasa.gov

Centralized Decentralized

Network Topology

Adapted from Linked by A. Barabàsi