patterns edgesystems
DESCRIPTION
All images and content courtesy of Bear KaufmanTRANSCRIPT
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 PatternsCollection
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 7 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