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Fractal image compression is a lossy technique with§high compression ratios, good quality, and fast§decoding. However, the computational complexity and§long coding time makes it unpractical. This book§introduces possible solutions for these problems.§In the book, A full quadtree and a full binary-tree§searchless fractal algorithms introduced in chapter 1§and 2. The full quadtree algorithm introduced in§chapter 3 has a simpler data structure allowing a§hardware implementation. The two-level quadtree§algorithm introduced in chapter 4 is an improved§version of chapter 3. Chapter 5 gives a two-level§fractal FPGA hardware architecture design§corresponding to chapter 3. Chapter 6 improves the§result of chapter 5 by employing 4 quadtree levels.§The most important findings of this book are: 1. The§algorithms fix the location of domain block. It§reduces the complexity of the fractal encoding. 2.§The algorithms can encode smaller range blocks, even§single pixels. This is unique among current fractal§algorithm implementations. 3. The algorithms arefaster than the traditional methods because of no§domain block searching. 4. The algorithms can be§transferred into FPGA hardware architecture.