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E-grāmata: Fractal Dimension of Architecture

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Fractal Dimension of ArchitecturePalielināt
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Fractal analysis is a method for measuring, analysing and comparing the formal or geometric properties of complex objects. In this book it is used to investigate eighty-five buildings that have been designed by some of the twentieth-century’s most respected and celebrated architects. Including designs by Le Corbusier, Eileen Gray, Frank Lloyd Wright, Robert Venturi, Frank Gehry, Peter Eisenman, Richard Meier and Kazuyo Sejima amongst others, this book uses mathematics to analyse arguments and theories about some of the world’s most famous designs.

Starting with 625 reconstructed architectural plans and elevations, and including more than 200 specially prepared views of famous buildings, this book presents the results of the largest mathematical study ever undertaken into architectural design and the largest single application of fractal analysis presented in any field. The data derived from this study is used to test three overarching hypotheses about social, stylistic and personal trends in design, along with five celebrated arguments about twentieth-century architecture. Through this process the book offers a unique mathematical insight into the history and theory of design.

Recenzijas

This book is a case-study displaying its strengths and weaknesses in testing hypotheses regarding the architecture of 85 homes from four continents designed by prominent architects between 1901 and the present day. Mathematicians will enjoy reading the results of the application of the box-counting method . the text is both well-written and remarkably error free . Thank you, authors and editors! (Joel Haack, MAA Reviews, February, 2018)







The authors give valuable critical thoughts about a few sensitive problems that researchers face when they use fractal dimension for analyzing images. 625 architectural plans and elevations (derived from the 85 buildings) are considered and interesting conclusions from the fractal and statistical analysis performed are brought to the reader's attention. (Elena Hadzieva, Mathematical Reviews, September, 2018)









It is written by experts who have published a lot on this particular subject on the boundary of architecture and mathematics. this book is in the first place addressing architect students or researchers . All the elements of the research methodology, hence also the fractal dimension, are clearly and extensively explained and motivated. Also the analysis of the results and conclusions are carefully described. So it is easy to read and understand for anyone interested in the topic. (Adhemar Bultheel, European Mathematical Society, euro-math-soc.eu, December, 2016)

1 Introduction
1(20)
1.1 Rationale and Aims
2(1)
1.2 Primary Hypotheses
3(2)
1.3 Secondary Hypotheses
5(2)
1.4 What Is a Fractal?
7(4)
1.5 Measuring Fractal Dimensions
11(2)
1.6 Book Structure
13(5)
1.7 Conclusion
18(3)
Part I Understanding and Measuring Fractal Dimensions
2 Fractals in Architectural Design and Critique
21(18)
2.1 The Problem of Defining `Fractal Architecture'
23(4)
2.2 Fractals in Architectural Design
27(8)
2.2.1 Architecture: Pre-formulation of Fractal Theory
28(2)
2.2.2 Post-formulation: Architecture Inspired by Fractals
30(2)
2.2.3 Fractally-Generated Architecture
32(3)
2.3 Conclusion
35(4)
3 Introducing the Box-Counting Method
39(28)
3.1 Introduction
39(18)
3.1.1 Mosque Window Detail
41(5)
3.1.2 The Robie House
46(4)
3.1.3 The Villa Savoye
50(5)
3.1.4 Comparison of Results
55(2)
3.2 The Application of Fractal Analysis to the Built Environment
57(8)
3.2.1 Urban Analysis
57(2)
3.2.2 Architectural Analysis
59(6)
3.3 Conclusion
65(2)
4 Measuring Architecture
67(20)
4.1 Introduction
69(1)
4.2 Philosophical Foundations
70(2)
4.3 Precision or Purpose
72(1)
4.4 Framework
73(9)
4.4.1 Level 1: Outline
75(1)
4.4.2 Level 2: Outline + Primary Form
76(2)
4.4.3 Level 3: Outline + Primary Form + Secondary Form
78(1)
4.4.4 Level 4: Outline + Primary Form + Secondary Form + Tertiary Form
79(2)
4.4.5 Level 5: Outline + Primary Form + Secondary Form + Tertiary Form + Texture
81(1)
4.5 Discussion
82(2)
4.6 Conclusion
84(3)
5 Refining the Method
87(48)
5.1 Introduction
88(3)
5.2 Image Pre-processing Test
91(19)
5.2.1 Field and Image Properties
91(1)
5.2.2 Field Properties
92(1)
5.2.3 Image Properties
93(1)
5.2.4 Test Description
94(7)
5.2.5 Data Analysis Method
101(1)
5.2.6 Results of the Pre-processing Test
101(7)
5.2.7 Discussion
108(2)
5.3 Image Processing Test
110(17)
5.3.1 Image Processing Factors
112(1)
5.3.2 Managing Limits
113(3)
5.3.3 Test Description
116(5)
5.3.4 Data Analysis Method
121(3)
5.3.5 Results and Discussion
124(3)
5.4 Revisiting the Robie House and the Villa Savoye
127(2)
5.5 Conclusion
129(6)
Part II Analysing Architecture
6 Analysing the Twentieth-Century House
135(24)
6.1 Introduction
135(1)
6.2 Research Description
136(8)
6.2.1 Data Selection
136(2)
6.2.2 Data Scope
138(1)
6.2.3 Data Source and Type
138(4)
6.2.4 Data Interpretation
142(1)
6.2.5 Data Representation
143(1)
6.2.6 Data Processing
144(1)
6.2.7 Data Settings
144(1)
6.3 Research Method
144(12)
6.3.1 Identifying and Coding Data
146(1)
6.3.2 Analysis of Each Building
146(1)
6.3.3 Analysis of a Set of Buildings
147(2)
6.3.4 Analysis of a Sub-set of Buildings
149(1)
6.3.5 Comparative Analysis
150(1)
6.3.6 Interpretation of Results
151(1)
6.3.7 Presentation of Results
152(4)
6.4 Additional Applications of the Method
156(1)
6.5 Conclusion
157(2)
7 The Rise of Modernity
159(46)
7.1 Functionalist Modernism
160(2)
7.2 Le Corbusier
162(16)
7.2.1 Pre-modern Houses (1905--1912)
162(3)
7.2.2 Pre-modern Houses, Results and Analysis
165(4)
7.2.3 Modern Houses (1923--1931)
169(2)
7.2.4 Modern Houses, Results and Analysis
171(6)
7.2.5 Comparing the Pre-modern and Modern Houses
177(1)
7.3 Eileen Gray
178(8)
7.3.1 Modern Houses (1926--1934)
179(3)
7.3.2 Gray, Results and Analysis
182(4)
7.4 Mies van der Rohe
186(7)
7.4.1 Modern Houses (1930--1951)
187(3)
7.4.2 Mies van der Rohe, Results and Analysis
190(3)
7.5 Comparison of the Three Modernists
193(3)
7.6 Testing `Form Follows Function'
196(8)
7.6.1 Orientation and Approach
197(1)
7.6.2 Method and Hypothesised Results
198(2)
7.6.3 Results and Discussion
200(4)
7.7 Conclusion
204(1)
8 Organic Architecture
205(38)
8.1 Organic Modernity
206(1)
8.2 Frank Lloyd Wright (1867--1959)
207(2)
8.3 Five Prairie Style Houses (1901--1910)
209(6)
8.3.1 Prairie Style Houses, Results and Analysis
210(5)
8.4 Five Textile-Block Houses (1923--1929)
215(7)
8.4.1 Results and Analysis of Wright's Textile-Block Houses
218(4)
8.5 Five Triangle-Plan Usonian Houses (1950--1956)
222(5)
8.5.1 Usonian Houses, Results and Analysis
224(3)
8.6 Comparing the Three Sets
227(3)
8.7 Wright's Style, Perceived and Measured
230(2)
8.8 Measuring Spatio-Visual Experience
232(9)
8.8.1 Alternative Perspective-Based Approaches
233(5)
8.8.2 Method and Results
238(3)
8.9 Conclusion
241(2)
9 The Avant-Garde and Abstraction
243(40)
9.1 The New York Five
244(2)
9.2 Peter Eisenman
246(8)
9.2.1 Five Houses (1968--1975) by Peter Eisenman
247(3)
9.2.2 Eisenman Houses, Results and Analysis
250(4)
9.3 John Hejduk
254(8)
9.3.1 Five Houses (1954--1963) by John Hejduk
256(3)
9.3.2 Hejduk Houses, Results and Analysis
259(3)
9.4 Richard Meier
262(8)
9.4.1 Five Houses (1967--1974) by Richard Meier
264(2)
9.4.2 Meier Houses, Results and Analysis
266(4)
9.5 Comparison of the Three Whites
270(4)
9.6 Frontality, Rotation and the Whites
274(6)
9.6.1 The Analytical Method
275(5)
9.7 Conclusion
280(3)
10 Post-modernism
283(30)
10.1 Post-modernity
284(2)
10.2 Robert Venturi and Denise Scott Brown
286(8)
10.2.1 Five Houses (1959--1990) by Venturi and Scott Brown
287(2)
10.2.2 Venturi and Scott Brown Houses, Results and Analysis
289(5)
10.3 Frank Gehry
294(9)
10.3.1 Five Houses (1978--1984) by Frank Gehry
296(4)
10.3.2 Frank Gehry's Houses (1978--1984), Results and Analysis
300(3)
10.4 Comparison of the Post-Modernist Works
303(3)
10.5 Formal Modelling and Functional Permeability
306(5)
10.5.1 The Analytical Method
306(2)
10.5.2 Results and Discussion
308(3)
10.6 Conclusion
311(2)
11 Minimalism and Regionalism
313(56)
11.1 Introduction
313(2)
11.2 Minimalism
315(2)
11.3 Kazuyo Sejima
317(9)
11.3.1 Five Houses (1994--2003) by Kazuyo Sejima
318(4)
11.3.2 Sejima Houses, Results and Analysis
322(4)
11.4 Atelier Bow-Wow
326(9)
11.4.1 Five Houses (1998--2004) by Atelier Bow-Wow
327(4)
11.4.2 Atelier Bow-Wow Houses, Results and Analysis
331(4)
11.5 Regionalism
335(3)
11.6 Peter Stutchbury
338(7)
11.6.1 Five Houses (2004--2011) by Stutchbury
339(2)
11.6.2 Stutchbury Houses, Results and Analysis
341(4)
11.7 Glenn Murcutt
345(14)
11.7.1 Five Early Houses (1975--1982) by Glenn Murcutt
346(3)
11.7.2 Murcutt, Early Houses, Results and Analysis
349(4)
11.7.3 Five Later Houses (1984--2005) by Glenn Murcutt
353(2)
11.7.4 Murcutt Later Houses, Results and Analysis
355(4)
11.8 Testing Visual Lightness and Transparency
359(6)
11.8.1 Method and Results for Test 1
360(2)
11.8.2 Method and Results for Test 2
362(1)
11.8.3 Discussion
363(2)
11.9 Comparative Results
365(3)
11.10 Conclusion
368(1)
12 Conclusion
369(30)
12.1 Presentation of Results
370(1)
12.2 Chronological Analysis
371(12)
12.2.1 Average Elevations
372(2)
12.2.2 Average Plans (Including Roofs)
374(1)
12.2.3 Average Plans (Excluding Roofs)
375(1)
12.2.4 Elevations and Plans Combined
376(2)
12.2.5 Elevation Ranges
378(1)
12.2.6 Plan Ranges (Including Roofs)
379(1)
12.2.7 Plan Ranges (Excluding Roof)
380(3)
12.3 Stylistic Period
383(5)
12.3.1 Averages
384(2)
12.3.2 Ranges
386(1)
12.3.3 Standard Deviation
387(1)
12.4 Formal Coherence
388(3)
12.5 Complexity and Consistency
391(4)
12.6 Conclusion
395(4)
References 399(20)
Index 419
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