Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Additional Information Glossary of Terms Links & Resources 

Lesson 1 – Page 2:
How pixels are colored Figure 2: Foisoun © 2005 Janet Parke
In Lesson 1 we're going to begin learning about the nature of fractals and exploring their amazing structure. There are many types of fractals. The three most common categories are: escapetime fractals – Mandelbrot, Lyapunov, Phoenix, Newton, etc.; Iterated Function Systems (called IFS fractals) – of which Flame fractals is a subset; and random fractals, which are generated by stochastic rather than deterministic processes. For the purposes of this course, we are going to focus entirely on escapetime fractals – the Mandelbrot and Julia structures, specifically. Once the basic concepts are learned using these fractal formulas, they can then be applied and adapted to explorations using other calculation formulas. Familiar fractal structures can then provide a benchmark for use in exploring the various coloring formulas. [Note: this lesson contains fractalspeak and mathematical terms that may be unfamiliar to you. Please check the Glossary (link above) for definitions and explanations. And be sure to let me know if there are terms I've missed or that are still unclear.] It's important to have at least a rudimentary understanding of how a fractal image appears on your computer screen. Escapetime fractals are rendered with a special type of formula that takes a complex number (a number which has two parts – a real part, and an imaginary part) – performs a specified set of actions upon that number, and then produces a result. The result is then iterated (fed back into the formula repeatedly) until some predetermined condition (called the bailout) is met. Once the bailout threshold is crossed and a numerical result has been determined, the coloring formula selected in Ultra Fractal uses that result to assign a color to the pixel. So... calculating and rendering a Mandelbrot fractal on your computer screen works like this:
Figure 3 (at left) is a 50 pixel by 25 pixel rendering of the image at the top of the page. Each pixel is a tiny point of color on the screen – much too small to see individually. 

Figure 4 
Figure 4 is a magnification of Figure 3, where each pixel is now expanded into a small block of color. For each pixel, the formula iterated until the bailout threshold was crossed, then the pixel was assigned the color you see in each block above. Every image is calculated and colored this way – one pixel at a time. 


Copyright © 20052011 Janet Parke 