The Beauty of Math
Guided only by their feeling for symmetry, simplicity, and generality, and an indefinable sense of the fitness of things, creative mathematicians now, as in the past, are inspired by the art of mathematics rather than by any prospect of ultimate usefulness.  
  —   E. T. Bell
Least Prime Factor - Spiral Method Blue
Mathematics is beautiful: From equations that express hidden relations to highly elegant proves! By combining algorithms and mathematical principles it is possible to generate images that impress through their stunning colors, shapes, and patterns, as well as the deep underlining mathematical secrets they reveal.

Mathematics and Art
Mathematics and art appear to be completely different areas: Art deals with the subjective perception of the human mind and encourages unbounded creativity, no rules, no order. Mathema- tics, on the other hand, establishes and reveals relations through logical deduction with clear definitions and order.

This website aims to combine both: Hidden patterns of mathema- tics become visible by applying simple or complex ideas of art. Simultaneously, we yield wonderful pieces of art by applying logical mathematical principles or algorithmic processes!
Endless Possibilities
The possibilities and opportunities to visualize complex or hidden structures and laws are limitless! Already basic ideas for art concepts yield wonderful images that reveal hidden relations.
By applying even more advanced techniques and algorithms you experience the true power of art and mathematics as a united field of research and creativity.

From prime numbers, Fibonacci numbers, sequences, series, functions, equations, shapes, recursions to random values - we can apply art concepts on countless aspects of mathematics. We get a completely new perspective and might even gain new knowledge.

We first need an algorithmic method to visualize mathematical concepts! These methods generate images based on a numerical input: box method, spiral method, walk method, graph method and so much more! The imagination is not limited. The concept of the different methods is explained in the corresponding section.
Pseude Dual Graph Visualization
Greatest Prime Factor - Spiral Method Green
Hidden Patterns
Mathematicians search for patterns and principles that lay deep in the foundations of the mathematical definitions. The union of art and mathematics enables humans to get a new perspective on numerous patterns and reveal completely new ones. Every beautiful aspect of an image is a mathematical question and any irregularity might result in a whole new theory!

Creative Algorithms
The essential part to create a stunning image and to visualize a mathematical secret is an algorithm, i.e. a method: It is extremely interesting to invent new methods that yield new images and reveal even more details. There is no limit to your creativity and no limit to the number of algorithms you can think about!
Web Applications
Besides the wonderful images that are available on this website, you can find various publically accessible web applications that allow you to create your own visualizations based on personal parameters and wishes, e.g. any equation or sequence you like. Those web applications are not only great in order to discover the united world of mathematics and art but enable you to investigate interesting features and images in further detail.

Research
Several methods yield images that reveal completely new details of mathematical aspects or produce unbelievable interesting and unexpected patterns. The visualizations do not only encourage further research on mathematical aspects but especially the understanding, description, and prediction of algorithmic methods: Why does mathematics shape some images in the way it does? Can we find the connections between mathematical input and the visualization output?
Walk Method: f(n) = 2*log(n)+4*n (mod 6), g(n) = 4*n+76
Prime Twins - Spiral Method Green on Red
Request Image
All images can be ordered in high quality and various sizes as professional poster or wall picture by sending an informal contact request via mail. The pictures combine mathematics and art in a stunning way. You can find several hundred images on our website so you definitely find the perfect image for your room or institute. The images are not only a treat for the eye but will emphasize your dedication to underlying principles and patterns!

Please keep in mind that the online shop is only a late extension due to many requests! The aim of this website is to investigate and combine mathematics with art accessible for everyone. If you want to support this website and want to have unique art pieces at home, feel free to discover the online shop!
About Beauty of Mathematics
This website was created by several international students of mathematics led by Fabian Schneider in mid-2017. The aim: To make mathematical visualizations, mathematical artwork, and algorithmic art publically accessible and concentrate the unlimited possibilities at one place! We want to inspire other people, fuel new mathematical research and emphasize the hidden beauty that lies deep inside the foundations of mathematics.

Several people contribute through ideas, new algorithms, and suggestions. Every person that has found interesting or useful methods to visualize mathematical aspects are invited to contribute and to get in touch with us!
Greatest Prime Factor - Box Method Green Scale