Download - Patterns edgesystems
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Patterns,Pattern Application,
& Edge
Courtesy of Bear Kaufmann
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Concentric Patterns
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Concentric:Growth
Tree Rings
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Concentric:Growth Through Accretion
Agate
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Too
Hot
Too
Cold
You
Are
Here
Solar System: Not To Scale
Concentric:Radiating & Diffusing Energy
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Radial PatternsCollection
Lupine - Lupinus polyphyllus
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Spiral Patterns
Medusa’s Head Cactus - Euphorbia caput-medusae
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Spirals:For Growth
Tide Pool
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Spirals in 3D:Helixes
Chayote Squash - Sechium edule
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The SpiralNote that each new square has a side which is as long as the sum of the latest two square's sides.
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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
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Phi•1.6180339887498948482045868343656381177203091798057628621354486227052604628189044970720720418939113748475408807538689175212663386222353693179318006076672635433389086595939582905638322661319928290267880675208766892501711696207032221043216269548626296313614438149758701220340805887954454749246185695…
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Oak Tree - Quercus spp.
Spirals in 3D:Helixes
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Argentinian Coast
Spirals:Turbulent Flow
earthobservatory.nasa.gov
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Interlocking Spirals:von Karman vortex streets
earthobservatory.nasa.gov
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Ideas for Application
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Ideas for Application
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Ideas for Application
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Interlocking Spirals
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Spirals in TimeDisturbance
Wave Patterns
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Spirals in TimeDisturbance
Wave Patterns
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Turbulence
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Streamlines
earth.google.com
Alaska
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Effects of Flow
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Flow
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Crenulations
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Crenulations:Maximize Edge
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Crenulations:Maximize Edge
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Crenulations:Habitat
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Surface Area to Volume
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Bucky
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Fractals:fractus = part
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Fractals:systems inside systems
patterns within patterns
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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
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Edible Fractals
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Fractals:Spirals
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Edge
The interface between two ecosystems represents a third, more complex,
system which combines both.
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Gradients:the rate of transition
Pressure
Temperature
Acidity
Elevation
& other properties
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Branches & Networks
Grape Leaf
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Branches
Fennel
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Leaves and Branching• Leaves are also found in groups of Fibonacci numbers.
• Branching plants always branch off into groups of Fibonacci numbers.
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Beech Tree
Branching:Dendritic
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Low Diffusion
Low Friction
Higher Diffusion
High Friction
Most Diffusion
For
Least Friction
Branches:For Diffusion and Accumulation
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Branches:oldest oaks have 7 orders
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Branches:Watersheds and Tributaries
Oakland Hills - Digital Elevation Model
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Branches:Water Flow
Jordan earthobservatory.nasa.gov
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Networks
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earthobservatory.nasa.gov
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Centralized Decentralized
Network Topology
Adapted from Linked by A. Barabàsi
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