Table Of Content— African----
— Fractals----
M O D E R N C O M P U T IN G
A N D IN D IG E N O U S D ESIG N
R O N EG LA SH
Contents
Acknowledgments ix
PART I Introduction
CHAPTER J Introduction to fractal geometry 3
CHAPTER 2 Fractals in African settlement architecture 20
CHAPTER 3 Fractals in cross-cultural comparison 39
CHAPTER 4 Intention and invention in design 49
PART II African fractal 7nathematics
CHAPTER 5 Geometric algorithms 61
CHAPTER 6 Scaling 71
CHAPTER 7 Numeric systems 86
/
CHAPTER 8 Recursion 109
CHAPTER 9 Infinity 147
CHAPTER IO Complexity 151
viii Contents
PART III Implications
Chapter 11 Theoretical frameworks in cultural studies of knowledge 179
chapter 12 The politics of African fractals 192
chapter 13 Fractals in the European history of mathematics 203
chapter 14 Futures for African fractals 216
appendix Measuring the fractal dimension of African settlement architecture 231
Notes 235
References 243
Index 253
•Acknowledgments
Thanks to go first to my wife, Nancy Campbell, who has tolerated my obsessions
with grace, and to Evelyn, Albert, and Joanne Eglash, who inspired many of them.
I am grateful for the assistance of my professors at UCSC: Ralph Abraham, Steve
Caton, James Clifford, Donna Haraway, Gottfried Mayer-Kress, Ken Norris, Heinz-
Ouo Peiigen, Carolyn Martin Shaw, and Patricia Zavella. Equally important were
my fellow UCSC graduate students, in particular David Bain, Julian Bleecker,
Peter Broadwell, Kirby Bunas, Claudia Castenada, Giovanna Di Chiro, Joe
Dumit, Vincente Diaz, Paul Edwards, Linda Garcia, Jennifer Gonzales, Chris Gray,
John Hartigan, Sharon Helsel, Laura Kang, Lorraine Kenny, Matthew Kobbe, Angie
Rosga, Warren Sack, Meg Satterthwaite, Sandy Stone, Marita Sturken, Bemt Wahl,
and Sarah Williams. Thanks also to Billie Harris, Miranda Hays, Rebecca Lyle,
Ken Martin, Sheila Peuse, Adolph Smith, Joshua Weinstein, and Paul Yi.
Research funding from the Institute for Intercultural Studies and the Ful-
bright program made possible my fieldwork in west and central Africa. As chap
ter 10 makes clear, 1 owe much to my Senegalese colleagues, Christine Stna Diatta
and Nfally Badiane. Also of great help in Senega! were Abdouli Ba, Real Basso,
Charles Becker, Kolado Cisse, Ibnou D'tagne, Pathe Diagne, Souleymane Bachir
Diagne, Mousse Diop, Waly Coly Faye, Max, Marie-Louise Moreau, Margot
Ndiaye, Victor Sagna, Ousinan Sen, Fatou Sow, Yoro Sylla, Sakir Thaim, and Riene
Acknowledgments
Toje. From the West African Research Center I received the expert advice of
American professors Eileen Julien and Janis Mays. Thanks also to Shamira
Johnson, Paul and Betsey Harney, Jane Hale,'Lisa McNee, and Liz Mermin.
I am also grateful to Issiaka Isaac Drabo and the brilliant Canadian pho
tography team, Michel et Didi, in Burkina Faso. Thanks also to Amadou
Coulibaly, Kalifa Kon£ and Abdoulaye Sylla in Mali. In Cameroon I received the
generosity of Ireke Bessike, Ngwa Emmanuel, Noife Meboubo, the late Engel
bert Mveng, and Edward Njock. My work in Benin would not have been possible
without the assistance of Tony Hutchinson; thanks also to Knke Alfred, Natheli
Roberts, and Martine de Sousa for their expertise in vodun. In Ghana Michael
Orlansky graciously introduced me to the many cultural resources available. Many
of the local folks 1 spoke to in west and central Africa, while extending great gen
erosity and enthusiasm, asked that their names remain unrecorded, and I thank
them as well.
On my return to the United States 1 received a fellowship from the Cen
ter for the Humanities at Oregon State University, which also offered the oppor
tunity to work with anthropologists Joan Gross, David Gross, and Cort Smith,
as well as Kamau Sadiki from the Portland Black Educational Center. Thanks also
to Michael Roberson for bis geometry advice, and David and Barbara Thomas
(now math teachers at Hendersonville High, North Carolina) for investigating
owari patcerns. A two month fellowship at the University of Oregon got me
through the summer, and into my current position at The Ohio State Univer
sity. Here I have been thankful for help from Patti Brosnan, Wayne Carlson,
Jacqueline Chanda, Cynthia Dillard, David Horn, Lindsay Jones, Okechukwu
Odita, Egondu Rosemary Onyejekwe, Robert Ransom, Dan Reff, Rose Kapian,
Carolyn Simpson, Daa’iyah I Saleem, Jennifer Terry, Cynthia Tyson, and
Manjula Waldron.
There are also many collegues, geographically scattered, whose feedback has
been invaluable. In particular 1 would like to thank Madeleine Akrich, Jack
Alexander, Mary Jo Arnoldi, George Arthur, Marcia Ascher, Jim Barta, Silvio
Bedini, TQ Berg, Jean-Paul Bourdier, Geof Bowker, Michael T. Brown, Pat
Caplin, Brian Casey, Jennifer Croissant, Don Crowe, Jim Crutchfield, Ubiratan
D'Ambrosio, Ronald Bell, Osei Darkwa, Marianne de Laet, Gary Lee Downey,
Munroe Eagles, Arturo Escobar, Florence Fasanelli, James Fernandez, Marilyn
Frankenstein, Rayvon Fouche, Paulus Gerdes, Chonat Getz, Gloria Gilmer,
David Hakken, Turtle Heart, Deborah Heath, David Hess, Stefan Helmreich, Dar-
ian Hendricks, David Hughes, Sandy Jones, Esmaeli Knteh, Roger P. Kovach, Gelsa
Knijnik, Bruno Latour, Murray Leaf, Bea Lumpkin, Robin Mackay, Caro! Malloy,
Benoit Mandelbrot, Mike Marinacci, Joanna Masingiia, Lynn McGee, James
Ac/cnowledgnien is
Morrow, David Mosimege, Brian M Murphy, Diana Baird N’Diaye, Nancy Nooter,
Karen Norwood, Spurgeon Ekundayo Parker, Clifford Pickover, Patricia Poole,
Arthur Powell, Dean Preble, Dan Regan, J i'm Rauff, Sal Restivo, Pierre Rondeau,
John Rosewall, Rudy Rucker, Nora Sabelli, Jnron Sampson, Doug Schuler, Patrick
(Rick) Scott, Rob Shaw, Enid Schildkrout, David Williamson Shaffer, Larry
Shirley, Dennis Smith, George Spies, Susan Leigh Star, Paul Stoller, Peter Tay
lor, Agnes Tuska, Gary Van Wyk, Donnell Walton, D M Warren, Dorothy Wash
burn, Helen Watson-Verran, Mark W. Wessels, Patricia S. Wilson, and Claudia
Zaslavsky. Last and not least, thanks to my editors at Rutgers, Doreen Valentine
and Martha Heller.
PART
-Introduction-----------------—
CHAPTER
Introduction-------------------------------------------
to--------------------------- :------------------- —
fractal------------------------------------------------
—geometry-----------------:----------------------------
Fractal geometry has emerged as one of the most exciting frontiers in the
fusion between mathematics and information technology. Fractals can be seen
in many of the swirling patterns produced by computer graphics, and they have
become an important new tool for modeling in biology, geology, and other nat
ural sciences. While fractal geometry can indeed take ur into the far reaches.
. of high-rech science, its patterns are surprisingly common in traditional African
designs, and some of its basic concepts are fundamental to African knowledge
systems. This book will provide an easy introduction to fractal geometry for
people without any mathematics background, and it will show how these same
categories of geometric pattern, calculation, and theory are expressed in
African cultures.
Mathematics and culture
For many years anthropologists have observed that the patterns produced in dif
ferent cultures can be characterized by specific design therr.es. In Europe and Amer
ica, for example, we often see cities laid out in a grid pattern of straight streets
and right-angle corners. Another grid, the Cartesian coordinate system, has
long been a foundation for the mathematics used in these societies. In many works
