Simple Fractals

Learn to create simple fractal patterns and understand the application of recursion and self-similarity concepts in shaders.

Overview

• Implement a horizontal gradient using UV as the factor.

Learning Objectives

• Understand the basic concept of self-similarity in fractal patterns.
• Learn to generate simple fractals in a fragment shader through iteration or recursion.
• Master the application of coordinate transformations (e.g., scaling, translation) in fractal generation.
• Understand how to control the number of iterations to adjust the complexity and detail of fractals.

Prerequisites

• uv-coordinates
• pattern-repetition

Inputs

• float u_time — Time in seconds.
• vec2 u_resolution — Canvas size in pixels.

Key Concepts

• Normalize pixel coordinates to UV.

vec2 uv = gl_FragCoord.xy / u_resolution.xy;

• A horizontal gradient uses a 0-1 factor (usually UV) to blend colors.

float t = uv.x;
vec3 color = vec3(t);

• Keep the factor inside [0,1].

t = clamp(t, 0.0, 1.0);

How To Implement (Step-by-step)

• distance = length(pos)
• fractal += circle * amplitude
• amplitude *= 0.5

Self-check

• Does it compile without errors?
• Does the output match the goal?
• Are key values kept in [0,1]?

Common Mistakes

• Clamp t into [0,1] when needed.
• Don’t use raw pixels without normalization.
• Make sure edge0 < edge1 for smoothstep().
• Change frequency by scaling before fract().