For this project I wanted something new. Something that involves art. A new type of art. I wanted to combine mathematics visuals with formulas so you can experiment and create your own art.

But how?

You change the numbers and exponents, add z or c, and create your own art. Your imagination is the limit. What I created is a fractal laboratory.

You can:

• Enter the data.
• View the shape.
• Download it as a PNG or SVG.

What is fractal art?

In simple terms, fractal art is digital art created using mathematical formulas and repeated patterns rather than drawing every shape manually.

In another way, fractal art is a form of art that uses mathematics to display perfect geometric shapes. That could not be created manually.

The fun part of the code:

The full code:

  

  

  Responsive Mathematical Fractal Generator
  
  



  

    

      
Fractal Generator
      
      

        Formula f(z, c):
        

      

      

        Fractal Type:
        

          
Mandelbrot Style (Vary c)
          
Julia Set (Fixed c, Vary z)
        
      

      

        Constant c (Real, Imaginary):
        
      

      

        Resolution / Iterations:
        

      

      

        Color Palette:
        

          
Electric Neon
          
Fire & Gold
          
Deep Ocean
          
Monochrome
        
      

      

        
Render
        
Reset
      

      

        
PNG
        
SVG
      
    

    

      

        
Ready
        
      
    
  

  

Explaining parts of the code:

HTML structure:

Fractal type selector:

  
Mandelbrot Style (Vary c)

  
Julia Set (Fixed c, Vary z)

What it does:

Lets the user switch between two mathematical approaches.

Interaction control

What it does:

Controls how many mathematical iterations are performed for each pixel.

Math.js

What it does:

It loads MathJS, which allows the webpage to understand mathematical expressions.

The renderFractal() function

This is the core of the project.

function renderFractal() {

The pixel-by-pixel calculation:

for (let py = 0; py < height; py++) {

  for (let px = 0; px < width; px++) {

And if you want to try it yourself here is a demo.

Who can benefit from it?

Artists:

Artists can experiment with new formulas to create their own.

I even experimented with a couple of formulas.

Research / experimentation

It could serve as a simple visualization environment for experimenting with families of interactive equations.

As art for webpages

UI developers can use the results for webpages to display them on.

In general, everyone is interested in art. Or this type of art.

How to start:

Start by simple formulas for example:

Z² + c

Or

Z³ + c

And expand with each step to become something like

Z³ + 4c² + 3z²

Why did I build it?

The purpose of the project is to show that mathematics could be used for very beautiful types of art.

It's easy and fun and could show the beauty of mathematics.

Conclusion

This project shows that art has many ways to be implemented. It's fun and could be done by anyone. Artist, programmers, and anyone interested.

And now you can also create your own type of art. With this project.