Embedded SoPC Design with Nios II Processor and Verilog Examples

CHAPTER 22

MANDELBROT SET FRACTAL ACCELERATOR

The Mandelbrot set can be used to generate interesting fractal images. The algorithm to determine whether a point is within the set is computation intensive and thus drawing the entire screen requires a significant amount of time. In this chapter, we design a system that can zoom in on a specific area of the set and display the fractal on a VGA screen. We implement the same algorithm using a software routine and a hardware accelerator and compare their performances.

22.1 INTRODUCTION

A fractal is a fragmented geometric shape that can be split into smaller parts, each of which has a similar (but not necessarily identical) appearance to the full shape. The boundary of the Mandelbrot set forms a fractal. A sample zoom sequence of the Mandelbrot set is shown in Figure 22.1. The initial image of the Mandelbrot set is shown at the top left. A small region is selected and magnified (i.e., “zoomed in”) to form the second image at the top right. The process is repeated two more times and the images are shown on the bottom. Note that the set has an elaborate boundary and the boundary does not simplify at any given magnification.

Despite the complexity of the image, the fractal is usually governed by simple mathematical equations, as in the Mandelbrot set. Studying the mathematical properties of fractals is beyond the scope of this book. We simply treat these equations as an algorithm to generate fractal images and discuss the computation procedure ...