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11.3. Fractal Pattern

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(Weitergeleitet von Fractal Pattern)

Fractals are a basic characteristic of a Biophilic Urbanism.


11 3 01 Fractal Pattern.jpg


Problem-statement: How can we generate more complex and beautiful patterns in design?


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Discussion: One of the most common patterns in nature, and also one of the most beautiful, is known as the fractal. The mathematician Benoit Mandelbrot coined the term to refer to structures that contain self-similar elements at different scales, which can be described with mathematical precision (and even re-generated on computer). He and other researchers found that very many patterns in nature do have this fractal structure — as do many traditional structures in human environments. Examples of common fractal structures include trees (the leaf vein is self-similar to the twig, which is self-similar to the branch, which is self-similar to the trunk, etc).


A common way of generating fractal patterns in a human design is the use of the motif. This can be a particular geometric shape (sometimes quite simple) that is repeated at small and large scales — like the arch patterns that are repeated many times at many scales in the photo at the beginning of this pattern, a section of the Alhambra in Spain.


11 3 02 Fractal Pattern.jpg
One of the simplest fractal patterns, a series of identical triangles repeated at many different scales.


Mathematical fractals close upon themselves, and possess self-similarity, where a magnified portion resembles the whole. Magnification can be performed an infinite number of times, and the form looks similar. Some natural shapes, such as fern leaves, cauliflowers, and the mammalian lung, are self-similar through several magnifications right down to their microstructure. Yet most natural fractals are not, and instead obey the weaker condition of “statistical self-similarity”. Magnified portions are not exact copies of the whole, but they share some of the same complex properties. The point is that even those “statistically self-similar” fractals never show emptiness at any magnification.


11 3 03 Fractal Pattern.jpg
Richly fractal patterns in another part of the Alhambra building, Spain. Photo: Quesada Jua via Wikimedia Commons.


Applying this notion to architecture, pre-industrial and vernacular buildings reveal complex detailed structure whenever any portion is magnified. Natural materials themselves possess substructure that shows up through magnification (see Complex Materials, below). Contrast this visual richness with industrial-minimalist materials, which can show emptiness after even the first magnification. This is a result of the quest for a smooth minimalism, which may be pleasing to some persons, but represents the opposite of fractal structure.


“Statistical self-similarity” results from a fractal adapting to external conditions; indeed, a requirement for geometrical adaptation is that strict lines and self-similarity need to be abandoned. This is the reason why many natural fractals are approximate in this sense. Fractal patterns that adapt to connections, local conditions, flows, etc. are richly complex, and thus can never be mathematically pure. Since adaptive architecture has to accommodate a variety of human needs, rather than fit some abstract geometrical ideal, its fractal expression is necessarily approximate. 1


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Therefore:

Use fractal patterns in the form of repeated motifs at different scales. These can be simple elements that are repeated, altered in scale, rotated, and otherwise worked into a complex and beautiful pattern.


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Integrate your fractal pattern into a Human-Scale Detail incorporating Construction Ornament.




¹ Yannick Joye has explored some of the beneficial impacts of architecture with a fractal structure — see e.g. Joye, Y. (2007). Fractal architecture could be good for you. Nexus Network Journal, 9(2), 311-320.



SECTION I:

PATTERNS OF SCALE


1. REGIONAL PATTERNS

Define the large-scale spatial organization…

1.1. POLYCENTRIC REGION

1.2. BLUE-GREEN NETWORK

1.3. MOBILITY CORRIDOR

1.4. 400M THROUGH STREET NETWORK

2. URBAN PATTERNS

Establish essential urban characteristics…

2.1. WALKABLE MULTI-MOBILITY

2.2. LEVEL CITY

2.3. PUBLIC SPACE SYSTEM

2.4. BIOPHILIC URBANISM

3. STREET PATTERNS

Identify and allocate street types…

3.1.URBAN GREENWAY

3.2. MULTI-WAY BOULEVARD

3.3. AVENUE

3.4. SHARED SPACE LANE

4. NEIGHBORHOOD PATTERNS

Define neighborhood-scale elements…

4.1. STREET AS CENTER

4.2. PEDESTRIAN SANCTUARY

4.3. NEIGHBORHOOD SQUARE

4.4. NEIGHBORHOOD PARK

5. SPECIAL USE PATTERNS

Integrate unique urban elements with care…

5.1. SCHOOL CAMPUS

5.2. MARKET CENTER

5.3. INDUSTRIAL AREA

5.4. HOSPITAL

6. PUBLIC SPACE PATTERNS

Establish the character of the crucial public realm…

6.1. PLACE NETWORK

6.2. WALKABLE STREETSCAPE

6.3. MOVABLE SEATING

6.4. CAPILLARY PATHWAY

7. BLOCK AND PLOT PATTERNS

Lay out the detailed structure of property lines…

7.1. SMALL BLOCKS

7.2. PERIMETER BLOCK

7.3. SMALL PLOTS

7.4. MID-BLOCK ALLEY

8. STREETSCAPE PATTERNS

Configure the street as a welcoming place…

8.1. STREET AS ROOM

8.2. TERMINATED VISTA

8.3. STREET TREES

8.4. STREET FURNISHINGS

9. BUILDING PATTERNS

Lay out appropriate urban buildings…

9.1. PERIMETER BUILDING

9.2. ARCADE BUILDING

9.3. COURTYARD BUILDING

9.4. ROW BUILDING

10. BUILDING EDGE PATTERNS

Create interior and exterior connectivity…

10.1. INDOOR-OUTDOOR AMBIGUITY

10.2. CIRCULATION NETWORK

10.3. LAYERED ZONES

10.4. PASSAGEWAY VIEW



SECTION II:

PATTERNS OF MULTIPLE SCALE


11. GEOMETRIC PATTERNS

Build in coherent geometries at all scales…

11.1. LOCAL SYMMETRY

11.2. SMALL GROUPS OF ELEMENTS

11.3. FRACTAL PATTERN

11.4. FRAMING

12. AFFORDANCE PATTERNS

Build in user capacity to shape the environment…

12.1. HANDLES

12.2. CO-PRODUCTION

12.3. FRIENDLY SURFACES

12.4. MALLEABILITY

13. RETROFIT PATTERNS

Revitalize and improve existing urban assets …

13.1. SLUM UPGRADE

13.2. SPRAWL RETROFIT

13.3. URBAN REGENERATION

13.4. URBAN CONSOLIDATION

14. INFORMAL GROWTH PATTERNS

Accommodate “bottom-up” urban growth…

14.1. LAND TENURE

14.2. UTILITIES FIRST

14.3. DATA WITH THE PEOPLE

14.4. INCREMENTAL SELF-BUILD

15. CONSTRUCTION PATTERNS

Use the building process to enrich the result…

15.1. DESIGN-BUILD ADAPTATION

15.2. HUMAN-SCALE DETAIL

15.3. CONSTRUCTION ORNAMENT

15.4. COMPLEX MATERIALS



SECTION III:

PATTERNS OF PROCESS


16. IMPLEMENTATION TOOL PATTERNS

Use tools to achieve successful results…

16.1. FORM-BASED CODE

16.2. ENTITLEMENT STREAMLINING

16.3. NEIGHBORHOOD PLANNING CENTER

16.4. COMMUNITY MOCKUP

17. PROJECT ECONOMICS PATTERNS

Create flows of money that support urban quality…

17.1. TAX-INCREMENT FINANCING

17.2. LAND VALUE CAPTURE

17.3. EXTERNALITY VALUATION

17.4. ECONOMIES OF PLACE AND DIFFERENTIATION

18. PLACE GOVERNANCE PATTERNS

Processes for making and managing places…

18.1. SUBSIDIARITY

18.2. POLYCENTRIC GOVERNANCE

18.3. PUBLIC-PRIVATE PLACE MANAGEMENT

18.4. INFORMAL STEWARDSHIP

19. AFFORDABILITY PATTERNS

Build in affordability for all incomes…

19.1. INTEGRATED AFFORDABILITY

19.2. COMMUNITY LAND TRUST

19.3. MULTI-FAMILY INFILL

19.4. SPECULATION TAX

20. NEW TECHNOLOGY PATTERNS

Integrate new systems without damaging old ones…

20.1. SMART AV SYSTEM

20.2. RESPONSIVE TRANSPORTATION NETWORK COMPANY

20.3. AUGMENTED REALITY DESIGN

20.4. CITIZEN DATA