Preface

Hello, I'm Ortiz, a 16-year-old boy from the small town of Chieti in Italy, and this is my first venture into generative art. My dream is to attend Politecnico di Milano to study design and eventually start my own business.

At the beginning of 2022, I encountered the concept of generative art for the first time. I couldn't imagine that using just code could create such unimaginable artworks that even a brush couldn't replicate. The incredible art fascinated me so much that I decided to dive headfirst into it. For the past two years, I've been studying generative coding, p5js, threejs, glsl, and much more, aiming to leave my mark on the digital canvas.

Now, after two years of fruitful exploration of generative coding, I present my first piece of work. I worked on this piece during my free time throughout the past year, and I believe it will resonate with someone who appreciates it.

Inspiration

"Mathematik ist die Königin der Wissenschaften, und Arithmetik ist die Königin der Mathematik" - Carl Friedrich Gauss

"Mathematics is the queen of sciences, and arithmetic is the queen of mathematics," proclaims this quote from the famous German mathematician. But what if I tell you that mathematics is something much greater?

Long before our time, Pythagoras contemplated the patterns in nature, much like harmonies in music, deriving from numbers as the fundamental essence of everything. He believed that mathematics permeates everything around us, omnipresent and not just the queen of all sciences but the empress of the cosmos. Later, many prominent figures in art and science embraced his ideas, including Turing, Plato, Haeckel, Zeising, and, of course, Leonardo Fibonacci. It was Fibonacci who first showed the remarkable harmony between mathematics and nature. The spiral named in his honor literally permeates everything around us: the horns of animals, the shells of mollusks, even the arrangement of leaves on a plant stem. All these seemingly complex patterns, it turns out, follow a simple equation.

Contemplating this, I decided that sooner or later, I would undoubtedly continue their work and reflect the beauty of mathematics on my canvas. Reflecting on where to begin my exploration, I encountered the fascinating phenomenon of mathematical form - the fractal.

A fractal is a self-repeating form, meaning the same basic form appears again and again. In other words, if you zoom in or out, the same form is visible everywhere. These self-similar cyclic mathematical constructions with fractal dimension occur quite often, especially among plants. The most well-known example is the fern.

Similar fern-like patterns are also found in many plants (broccoli, Romanesco cabbage, tree branches, and leaves of plants), animals (mosses, corals, hydrozoa, sea stars, sea urchins), and even in the branching structure of blood vessels and bronchi in animals and humans. As you can see, fractals are literally ubiquitous. That's why I couldn't ignore this amazing and enchanting form of mathematical revelation.

Project philosophy

Welcome to the world of the boundless beauty of the Mandelbrot fractal, where mathematics transforms into art.

In this exploration, I approached the Mandelbrot fractal as if it were a picturesque, infinite landscape embodying the harmony between chaos and order, nature, and mathematics. Delving into the study of the fractal, one can capture striking similarities between the patterns and the world around us. Some may see turbulent river whirlpools in the pattern, some may see lightning bolts in the endless sky, and some may see a blossoming branch of sakura, endowing everyone with its incredible beauty, but hardly anyone will remain indifferent to such a wonderful image described by all one equation: “z = z² + c”.

Each line of this code is not just a command but an invisible hand inspired by nature itself, creating paintings where space and time dance in harmony. Every curve, every shadow, every color shift is the result of long hours of creativity and interaction with the boundless beauty of the Mandelbrot pattern.

Fractal Symphony is an immersion into a virtual space where infinite spirals and captivating patterns become the protagonists of each canvas. Fractal Symphony is a journey into the boundless world of shapes and colors, where the boundaries between mathematics and aesthetics blur. Fractal Symphony is the visualization of the harmony between precise calculations and the chaotic beauty of the universe that surrounds us.

Live Render Controls and Settings

If you feel like experimenting manually, finding your own fractal points, and adjusting them, I've provided full control over the canvas and fractal configuration.

• Menu Access: Click the arrow in the upper-left corner to open the menu. Here, you can export the fractal image in JPG format, edit and copy the current fractal configuration, paste a new fractal configuration, and reset the editing if needed.

• Image Manipulation: Press 1 to explore a new fractal area. Press 2 to change the shape of the fractal petals. Press 3 to change the fractal color scheme. Press spacebar to make the token static.

• Canvas Manipulation: You can interact with the canvas by using either the mouse or the keyboard. Use W, A, S, D, Q, E to move around the canvas. Mouse scroll controls zoom.

• Infinite Gallery Mode: Press 0 to toggle the infinite gallery mode. New fractals will be generated one after another, replacing the previous ones.

---

Since my father became visually impaired, my family has found itself in a rather challenging financial situation. I wholeheartedly appreciate everyone who supports me as an author and acquires tokens of Fractal Symphony. It means a lot to me. With your help, I hope to accumulate enough funds for my father's surgery. That would be wonderful.

I wish good health to everyone who reads this and their loved ones!