Designing with Algorithms: A Mathematical Guide

Computing is revolutionizing the creative process, transforming how designers approach ideation, prototyping, fabrication, communication, and representation. Yet many lack the foundational knowledge needed to fully harness its potential. Designing with Algorithms: A Mathematical Guide bridges this gap, offering a comprehensive, step-by-step exploration of algorithmic practices applicable across diverse design fields. This guide begins with foundational theories, illuminating the role of mathematics and computational logic in design thinking. It progresses to practical techniques for creating parametric 2D and 3D geometries, grid systems, patterns, forms, and fonts. The book culminates in real-world case designs, showcasing diverse applications of generative algorithms across urban design, architecture, graphic design, typography, fashion, and more. Unlike software-specific guides, this book emphasizes process and adaptability, teaching readers to think algorithmically and develop skills transferable to any programming platform. Whether you’re a student, practitioner, or enthusiast, this book empowers you to future-proof your design practice and unlock the creative potential of computation.

Table of Contents:
1. Algorithmic Thinking: Redefining Design Through Computation 2. Parametric Geometires 3. Transformative Geometries 4. Rule-Based Grid and Pattern Systems 5. Transformative Patterns 6. Multiverse of Mathematical Forms 7. Case Designs Conclusion: The Furture of Algorithmic Design

About the Author :
Arash Soleimani is Professor and Chair of Design Computation and Applied Computer Science—Media Arts at Woodbury University’s School of Architecture in Los Angeles, California. He holds a multidisciplinary PhD in Architectural Robotics from Clemson University’s School of Architecture, where his research intersected electrical and computer engineering, materials science and engineering, education, and human factors psychology. He also earned a Master of Architecture from the University of Nottingham, UK, with a focus on Responsive and Interactive Environments in Museums—a subject on which he published a book. His academic journey in design began with a Bachelor of Architecture from Isfahan University of Art, Iran.

Review :
"Designing with Algorithms: A Mathematical Guide takes a foundational approach to computational thinking and algorithmic design. Dr. Soleimani begins with clear explanations of how algorithms work, the basic types of algorithms and their systems of notation. He then uses this framework to move from the algorithm of cheese and tomato sandwich to explanations of parametric color and mathematical transformations. Each chapter builds on the previous allowing for the foundations set in the early chapters to enable the understanding of the increasingly complex topics such as fractals and diffusion. The focus on algorithms and mathematics over software specific instruction allows this book to work in a variety of settings and applications. I would highly recommend this book for faculty looking to provide their students with a strong foundation in algorithmic design and for professionals looking to evolve their practice." Mark Ericson, Professor of Architecture, Woodbury University "In a world increasingly defined by complexity, where systems are interconnected yet often unpredictable, Designing with Algorithms brings order to the chaos. Arash Soleimani invites designers from all disciplines to explore where creativity, mathematics, and computation converge, unlocking the power of algorithmic design. From parametric geometries to chaotic systems, this book teaches not just techniques, but a way of thinking that will reshape creative activity." Dr. Keith Evan Green, McLean Professor of Human Centered Design and Professor of Mechanical & Aerospace Engineering, Cornell University