The document discusses various types of patterns found in nature, including concentric, radial, spiral, fractal, branching, and network patterns. Specific examples are given to illustrate each type of pattern, such as tree rings, agate formations, solar systems, flowers, shells, hurricanes, trees, leaves, rivers, and coastlines. The patterns are described as ways that natural systems organize themselves and maximize factors like growth, diffusion, habitat space, and resource distribution.

1. Patterns, Pattern Application, & Edge Courtesy of Bear Kaufmann

2. Concentric Patterns

3. Concentric: Growth Tree Rings

4. Concentric: Growth Through Accretion Agate

5. Concentric: Radiating & Diffusing Energy Too Hot Too Cold You Are Here Solar System: Not To Scale

6. Radial Patterns Lupine - Lupinus polyphyllus

7. Spiral Patterns Medusa’s Head Cactus - Euphorbia caput-medusae

8. Spirals: For Growth Tide Pool

9. Spirals in 3D: Helixes Chayote Squash - Sechium edule

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

13. Spirals in 3D: Helixes Oak Tree - Quercus spp.

14. Spirals: Turbulent Flow Argentinian Coast earthobservatory.nasa.gov

15. Interlocking Spirals: von Karman vortex streets earthobservatory.nasa.gov

16. Ideas for Application

17. Ideas for Application

18. Ideas for Application

19. Interlocking Spirals

20. Spirals in Time Disturbance Wave Patterns

21. Spirals in Time Disturbance Wave Patterns

22. Turbulence

23. Streamlines earth.google.com Alaska

24. Effects of Flow

25. Flow

26. Crenulations

27. Crenulations: Maximize Edge

28. Crenulations: Maximize Edge

29. Crenulations: Habitat

30. Surface Area to Volume

31. Bucky

32. Fractals: fractus = part

33. Fractals: systems inside systems patterns within patterns

34. 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

35. Edible Fractals

36. Fractals: Spirals

37. Edge The interface between two ecosystems represents a third, more complex, system which combines both.

38. Gradients: the rate of transition Pressure Temperature Acidity Elevation & other properties

39. Branches & Networks Grape Leaf

40. Branches Fennel

42. Branching: Dendritic Beech Tree

43. Branches: For Diffusion and Accumulation Low Diffusion Low Friction Higher Diffusion High Friction Most Diffusion For Least Friction

44. Branches: oldest oaks have 8 orders

45. Branches: Watersheds and Tributaries Oakland Hills - Digital Elevation Model

46. Branches: Water Flow Jordan earthobservatory.nasa.gov

47. Networks

48. earthobservatory.nasa.gov

49. Network Topology Centralized Decentralized Adapted from Linked by A. Barabàsi