David Mumford has been University Professor in the Division of Applied Mathematics at Brown University since 1996. Before that he was at Harvard University for thirty-five years. He has been a contributor to the Calculus Textbook Project, led by Hughes-Hallett and Gleason. Over his long and distinguished career, Professor Mumford has received many awards and honours, including the Fields Medal in 1974, the Wolf Prize in 1998 and the National Medal of Science in 2010. Caroline Series is Professor of Mathematics at Warwick University where she currently holds an EPSRC Senior Research Fellowship. She was Kennedy Scholar at Harvard University from 1972 to 1974. In addition to technical publications, she has contributed widely to the popularization of mathematics. In 2014, she won the first Senior Anne Bennett Prize of the London Mathematical Society for contributions to mathematics and to the advancement of female mathematicians. She edits the new International Women in Maths website http://www.mathunion.org/wim/. David Wright is Professor at Oklahoma State University. He has held a guest professorship at the University of Göttingen, and was Sloan Fellow at the Institute for Advanced Study in Princeton from 1988 to 1990. From 1997 to 1999 he helped establish the famous William Lowell Putnam Mathematical Competition. In 2009 he received a Distinguished Teaching Award from the Mathematical Association of America.

'[This book is] richly illustrated with these wonderful and mysterious pictures and gives detailed instructions for recreating them, right down to the level of computer programs (written in pseudo-code, and easy to translate into any computer language) … the reader who attempts any substantial subset of [the projects] will gain enormously … Even those who are convinced they have no ability to visualize may change their minds … It is almost required reading for the experts in the field … I truly love this book.' John H. Hubbard, The American Mathematical Monthly

• Preface; Introduction; 1. The language of symmetry; 2. A delightful fiction; 3. Double spirals and Möbius maps; 4. The Schottky dance; 5. Fractal dust and infinite words; 6. Indra's necklace; 7. The glowing gasket; 8. Playing with parameters; 9. Accidents will happen; 10. Between the cracks; 11. Crossing boundaries; 12. Epilogue; Index; Road map.

David Mumford has been University Professor in the Division of Applied Mathematics at Brown University since 1996. Before that he was at Harvard University for thirty-five years. He has been a contributor to the Calculus Textbook Project, led by Hughes-Hallett and Gleason. Over his long and distinguished career, Professor Mumford has received many awards and honours, including the Fields Medal in 1974, the Wolf Prize in 1998 and the National Medal of Science in 2010. Caroline Series is Professor of Mathematics at Warwick University where she currently holds an EPSRC Senior Research Fellowship. She was Kennedy Scholar at Harvard University from 1972 to 1974. In addition to technical publications, she has contributed widely to the popularization of mathematics. In 2014, she won the first Senior Anne Bennett Prize of the London Mathematical Society for contributions to mathematics and to the advancement of female mathematicians. She edits the new International Women in Maths website http://www.mathunion.org/wim/. David Wright is Professor at Oklahoma State University. He has held a guest professorship at the University of Göttingen, and was Sloan Fellow at the Institute for Advanced Study in Princeton from 1988 to 1990. From 1997 to 1999 he helped establish the famous William Lowell Putnam Mathematical Competition. In 2009 he received a Distinguished Teaching Award from the Mathematical Association of America.

'[This book is] richly illustrated with these wonderful and mysterious pictures and gives detailed instructions for recreating them, right down to the level of computer programs (written in pseudo-code, and easy to translate into any computer language) … the reader who attempts any substantial subset of [the projects] will gain enormously … Even those who are convinced they have no ability to visualize may change their minds … It is almost required reading for the experts in the field … I truly love this book.' John H. Hubbard, The American Mathematical Monthly

• Preface; Introduction; 1. The language of symmetry; 2. A delightful fiction; 3. Double spirals and Möbius maps; 4. The Schottky dance; 5. Fractal dust and infinite words; 6. Indra's necklace; 7. The glowing gasket; 8. Playing with parameters; 9. Accidents will happen; 10. Between the cracks; 11. Crossing boundaries; 12. Epilogue; Index; Road map.