Key Parameters used in Algorithmic Art

We have previously seen how we can use fractals to generate art. Today we will briefly understand the key parameters which can be manipulated to generate a large variety of art.

• Fractal Formula / Function:

  • The core mathematical equation (e.g., Mandelbrot, Julia sets) that defines how points in space are iteratively transformed.

  • Different formulae produce different types of fractals.

• Iteration Depth / Max Iterations:

  • Number of times the formula is applied to each point.

  • Higher values produce more detail but increase rendering time.

• Zoom Level / Scale:

  • Determines the depth into the fractal being viewed.

  • Higher zoom reveals more intricate patterns, often unseen at lower levels.

• Escape Radius / Threshold:

  • A value that determines when to stop iterating a point if it diverges.

  • Commonly set to 2 for many fractal types, like the Mandelbrot set.

• Color Mapping / Palette:

  • Translates the number of iterations at each point into colors.

  • Affects visual aesthetics; smooth gradients or sharp transitions can create different moods.

• Seed / Starting Point (mainly for Julia sets):

  • The initial complex value that influences the fractal’s shape.

  • Changing the seed drastically alters the output in Julia sets.

• Bailout Conditions:

  • Criteria used to determine whether a point stays in the set or escapes.

  • Can include distance, angle, or other complex metrics.

    
    

It is fun experimenting with changes in these parameters and visualizing how it affects the art generated. Are there other parameters that you have been using?