''The Fractal Dimension of Architecture'' is a book that applies the mathematical concept of

fractal dimension In mathematics, a fractal dimension is a term invoked in the science of geometry to provide a rational statistical index of complexity detail in a pattern. A fractal pattern changes with the Scaling (geometry), scale at which it is measured. It ...

to the analysis of the architecture of buildings. It was written by Michael J. Ostwald and Josephine Vaughan, both of whom are architecture academics at the

University of Newcastle (Australia) The University of Newcastle is a public university in Newcastle, New South Wales, Australia. Established in 1965, it has a primary campus in the Newcastle suburb of Callaghan. The university also operates campuses in Central Coast, Singapore, ...

; it was published in 2016 by

Birkhäuser Birkhäuser was a Swiss publisher founded in 1879 by Emil Birkhäuser. It was acquired by Springer Science+Business Media in 1985. Today it is an imprint used by two companies in unrelated fields: * Springer continues to publish science (parti ...

, as the first volume in their Mathematics and the Built Environment book series.

Topics

The book applies the

box counting Box counting is a method of gathering data for analyzing complex patterns by breaking a dataset, object, image, etc. into smaller and smaller pieces, typically "box"-shaped, and analyzing the pieces at each smaller scale. The essence of the pr ...

method for computing fractal dimension, via the ArchImage software system, to compute a fractal dimension from

architectural drawing An architectural drawing or architect's drawing is a technical drawing of a building (or building project) that falls within the definition of architecture. Architectural drawings are used by architects and others for a number of purposes: to deve ...

s (elevations and floor plans) of buildings, drawn at multiple levels of detail. The results of the book suggest that the results are consistent enough to allow for comparisons from one building to another, as long as the general features of the images (such as margins, line thickness, and resolution), parameters of the box counting algorithm, and statistical processing of the results are carefully controlled. The first five chapters of the book introduce fractals and the fractal dimension, and explain the methodology used by the authors for this analysis, also applying the same analysis to classical fractal structures including the

Apollonian gasket In mathematics, an Apollonian gasket, Apollonian net, or Apollonian circle packing is a fractal generated by starting with a triple of circles, each tangent to the other two, and successively filling in more circles, each tangent to another three ...

Fibonacci word A Fibonacci word is a specific sequence of Binary numeral system, binary digits (or symbols from any two-letter Alphabet (formal languages), alphabet). The Fibonacci word is formed by repeated concatenation in the same way that the Fibonacci num ...

Koch snowflake The Koch snowflake (also known as the Koch curve, Koch star, or Koch island) is a fractal curve and one of the earliest fractals to have been described. It is based on the Koch curve, which appeared in a 1904 paper titled "On a Continuous Cur ...

, Minkowski sausage,

pinwheel tiling In geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A m ...

terdragon A dragon curve is any member of a family of self-similar fractal curves, which can be approximated by recursive methods such as Lindenmayer systems. The dragon curve is probably most commonly thought of as the shape that is generated from repea ...

, and

Sierpiński triangle The Sierpiński triangle, also called the Sierpiński gasket or Sierpiński sieve, is a fractal with the overall shape of an equilateral triangle, subdivided recursion, recursively into smaller equilateral triangles. Originally constructed as a ...

. The remaining six chapters explain the authors' choice of buildings to analyze, apply their methodology to 625 drawings from 85 homes, built between 1901 and 2007, and perform a statistical analysis of the results. The authors use this technique to study three main hypotheses, with a fractal structure of subsidiary hypotheses depending on them. These are *That the decrease in the complexity of social family units over the period of study should have led to a corresponding decrease in the complexity of their homes, as measured by a reduction in the fractal dimension. *That distinctive genres and movements in architecture can be characterized by their fractal dimensions, and *That individual architects can also be characterized by the fractal dimensions of their designs. The first and third hypotheses are not convincingly supported by the analysis, but the results suggest further work in these directions. The second hypothesis, on distinctive fractal descriptions of genres and movements, does not appear to be true, leading the authors to weaker replacements for it.

Audience and reception

The book is aimed at architects and architecture students; its mathematical content is not deep, and it does not require much mathematical background of its readers. Reviewer Joel Haack suggests that it could also be used for general education courses in mathematics for liberal arts undergraduates.

References

{{DEFAULTSORT:Fractal Dimension Of Architecture, The Fractals Architecture books Mathematics books 2016 non-fiction books Birkhäuser books

Topics

Audience and reception

Further reading

References