dr. wei songlin, dr. cyril fleurant, & dr. jon bryan ... · presented is an approach to...

Replicating Fractal Structures with the Reverse Box Counting Method: An Urban South-east Asian Example

May 2012

Dr. Wei Songlin, Dr. Cyril Fleurant, & Dr. Jon Bryan Burley

MSU started teaching exterior design as a college course in the 1860s, and began offering an undergraduate degree in LA 1898, with the first

student graduating in 1902.

Typical reforestation methods Typical methods of reforestation on reclaimed surface mines include; simple row plantings (image to right), gestalt method, and ecological field method Problems Row plantings are simple and cost effective however, they do not achieve a naturally appearing landscape Gestalt methods are heuristic in nature where one creatively merges and combines patterns together, until a desired condition is achieved

Ecological field laboratory methods use scientific measures such as frequency, density, and size to construct patterns

Origin of fractals

The Peano curves, the first observed fractal objects, could fill a void through a series of iterations utilizing only a few simple rules (Mandelbrot, 1982) French mathematician Benoit Mandelbrot created the term fractal (from the Latin word fractus, meaning broken) to describe the objects where irregularity separates them from typical Euclidian geometry curves

Image retrieved from http://www.physics.mcgill.ca/~gang/multifrac/index.htm

Further descriptions illustrating fractals

Cantor’s Dust Cantor’s dust has the geometric property where as the total length increases towards infinity.

Cantor’s Dust fractal object

Saturn’s ring was originally thought to be one entity, however, with the advancement of telescopic power it was discovered that the “ring” was in fact made up of

many smaller rings.

Fractal dimensions Fractal dimensions have values which cannot be expressed by a simple point or line.

Fractal dimensions attempt to quantify a subjective feeling which we have about how densely the fractal object fills the space in which it lies. They also provide a means for comparing the complexity of different fractals. Real fractal objects are different from theoretical ones. Only theoretical fractal objects can be explained by the self similarity equation.

Equation for the fractal dimension of a line

Equation for the fractal dimension of an area

Equation for the fractal dimension of self-similar objects Where: n = the number of subsets counted during the scaling process using a factor 1/k (self-similarity factor). k = number of iterations

Box-Counting Method: a tool for replicating

landscapes This process can estimate the fractal dimension of a real object! The natural object is covered with a grid of size r and one counts the number of boxes, N(r) that contain some part of the object. The value of “r” is progressively reduced and N(r) is similarly re-measured. As “r” tends to be very small values (0 in a theoretical way) one finds that log(N(r))/log(1/r) becomes the fractal dimension of the object (Fleurant et al., 2009).

This image illustrates the value of “r”

Equation for the fractal dimension of an object using the Box-Counting Method

Planning and design applications

There is a belief that fractals may have the ability to re-create complex landscape patterns that are hard to replicate with Euclidian geometry because the landscape is full of fractals: rivers, trees, landscape networks in general (Barnsley, 1993)

In landscapes it has always been relatively simple to describe an existing pattern, but hard to

replicate that pattern. Presented is an approach to replicate landscape patterns and a practical approach towards the use of fractals.

Application of the Inverse Box-Counting Method to reproduce a housing pattern in Lamma

Island, Hong Kong.


Lamma Island, Hong Kong.


Box Counting.


Results: The first empty boxes occurred when the box size was 162.5

meters. When the box size was reduced to 20.3125 meters, each structure was in its own box . In our study the resulting fractal number was 1.115, with 480 boxes filled across 4,096 boxes. Therefore approximately 11.7% of the boxes are filled.


Results: Replication

Enjoy your journey- maybe we shall travel together. Thank-you.

(copyright 1997, 2004, 2005, 2006, 2008, 2010, 2011 Dr. Jon Bryan Burley All Rights Reserved) (copyright 2011 Shawn Partin All Rights Reserved, used by permission)

Concordance Between Photographs and Computer Generated 3D Models In A Michigan

Highway Transportation Setting

Dr. Jon Bryan Burley, FASLA

with S. Partin, Dr. R. Schutzki, & Dr. P. Crawford Landscape Architecture

School of Planning, Design, and Construction Michigan State University E. Lansing, MI 48824 USA

[email protected], http://www.spdc.msu.edu/la May 2012

Everyone has a journey and story too

Lived in the UP, Northern Wisconsin, and Alberta, Canada Desired to be a professor since age 6; Since age 17 desired to be a scholar in landscape architecture; Teaching since 1975; BLA 1978 U of Minnesota; Registered LA 1982 Minnesota; MLA 1988 U of Manitoba; PhD 1995 in LA U of Michigan; Teaching and Scholarship as goals.

hobbies

Jon Bryan Burley

Gardening 5,000 books Lead Guitar Collect Hornby Trains Oil Painting Field Sketching

In this presentation, I discuss: 1. Recent work by Shawn Partin to

study human perception of computer generated images.

.

Since 1969, with the start of Elwood Shafer’s work, landscape architects, recreation scientists, and environmental psychologists have conducted research to develop predictive models to understand visual quality.

Structural Research Framework.

Landscape People

Photographs Respondent Preferences

Regression Analysis

Construct Construct

Independent Variables Dependent Variable

Rachel Kaplan School of Behavioral and Environmental Research

The methods include measuring the attributes of images.

Azores

Q-sort method produces respondent scores with a broad spread of values from the most preferred images to the least preferred images.

Each respondent evaluates 5 sets of 10 photographs.

Fast and easy for data sets with 250 to 500 images. Easy to repeat and replicate.

1 2 3 4 5 6 7 8 9 10

Most preferred Least preferred

(copyright 1997, 2004, 2005, 2006, 2008 Dr. Jon Bryan Burley All Rights Reserved)

In 1997 and 2011, reported general equations which explain between 67-79 percent of respondent preference (North American, French, and Portuguese), with an overall p-value for the equation <0.0001 and a p-value < 0.05 for each regressor.


Also in 2010 and 2011 we constructed a validated map of visual quality for a study area in Michigan.


In 2011 we studied the visual impact of new design for Detroit Michigan.

Researchers have discovered that the real landscape, black and white photographs, color photographs, and video covary well together.

However, drawings do not predict visual quality as the respondents evaluate the quality of the drawing, not the contents of the landscape. Copyright 2002 Jon Bryan Burley, all rights reserved


Shawn Partin was interested in examining the respondent perception of of Sketch-up Images.

Were the computer images perceived in a manner similar to photographs or were they more like drawings?

Shawn worked for the Michigan DOT.


Shawn Partin developed 25 pairs.

Seeded with 50 images from studies by Burley.

The statistical test is Kendall’s Coefficient of Concordance.

W statistics compared to a Chi-square value.

Chi-square = 39.364 at p<0.025. W = 40.164 at 24 df Since 40.164 is greater than 39.364, the

images are in concordance. The computer images are significantly similar to photographs as perceived by the respondents.

The statistical test is Kendall’s Coefficient of Concordance.

W statistics compared to a Chi-square value.

Chi-square = 79.490 at p<0.005. W = 86.290 at 49 df Since 86.290 is greater than 79.490, the

images are in concordance. The seeded set is significantly similar to evalutions by past respondents.

The science of visual quality and environmental quality evaluation has made significant strides over the last 45 years. Visual/environmental quality is measurable and predictable. Numerous science based applications exist to evaluate landscape change, landscape transformation, landscape disturbance, and landscape reclamation.

Concluding Statements

(copyright 1997, 2004, 2005, 2006, 2008, 2010, 2011 Dr. Jon Bryan Burley All Rights Reserved)

Acknowledgements I would like to thank: Shawn Partin, Di Lu, Mary Noffke, Jason Rokos, and Amy Mazure, former research assistants and students and now practicing landscape architects. Thomas Panagopoulos and Luis Loures, FERN, Universidade do Algarve, Faro. Portugal. Gaelle and Marjorie from INH-Paysage. Mo Fei from Tongji University, Shanghai, P.R. of China. Landscape Architecture Program and School of Planning, Design, and Construction, Michigan State University

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