Images

All images copyright Christopher Laplante unless otherwise noted. Usage or reproduction of any kind is prohibited without permission.

Chapter 1

Fig 1.3. The Mandelbrot Set

Fig 1.4. Bifurcation diagram for \(f(x) = x^2 + c\) with \(x=0\) and \(c\) swept from \(-2.0\) to \(1.0\)

Chapter 2

Fig 2.3. Julia set for \(f(z) = cos(z)\)

Fig 2.4. Douady’s rabbit

Fig 2.5. Inferno color scheme

Fig 2.6. Douady’s rabbit created using 10 iterations

Fig 2.7. Inferno color scheme utilization (dashed box) for Douady’s rabbit with 10 iterations. Note how the darker colors on the left are not used because the escape iteration count starts at 3

Fig 2.8. Douady’s rabbit created using 50 iterations

Fig 2.9. Inferno color scheme utilization (dashed box) for Douady’s rabbit with 50 iterations

Fig 2.10. Douady’s rabbit created using 200 iterations

Fig 2.11. Douady’s rabbit created using 800 iterations

Fig 2.12. Douady’s rabbit created using 800 iterations with histogram coloring

Fig 2.13. A Siegel disk

Fig 2.14. A dragon

Fig 2.15. The Julia set of \(sin(z)\)

Fig 2.17. The Mandelbrot Set

Chapter 3

Fig 3.4. Seals

Fig 3.5. An amoeba-like image generated from the filled Julia set of \(f(z) = Z^2+ .3-4i\)

Fig 3.6. A fern leaf

Fig 3.7. A fern leaf generated via IFS

Fig 3.8. IFS Representation of a tree

Fig 3.9. A forest of randomly generated fractal trees

Fig 3.10. A redwood forest

Fig 3.11. Green seaweed

Fig 3.12. Four-petaled flower from the Julia set of \(f(z) = z^2+0.384\)

Fig 3.13. Another four-petaled flower from the Julia set of \(f(z) = z^2+0.2541\)

Fig 3.14. A fractal storm cloud

Fig 3.15. "Three-dimensional" fractal clouds

Fig 3.16. Fractal rocks using same IFS codes as the clouds

Fig 3.17. Snowflakes generated by mandel_julia.rs

Fig 3.18. A snow fall generated by fall.rs

Fig 3.20. A randomly generated view of space

Fig 3.22. Dendrite structure generated by \(f(z) =z^2 + i\)

Fig 3.23. An EKG output simulated using a Julia set

Chapter 4

Fig 4.1. Castle

Fig 4.2. A fractal maze

Fig 4.3. "Winter reflections" by waferboard is marked with CC BY 2.0. To view the terms, visit https://creativecommons.org/licenses/by/2.0/?ref=openverse. Originally in color.

Fig 4.4. Computer generated equivalent of swampy pond shown in "winter reflections"

Fig 4.6. Bifurcation diagram for model economic system

An example Game of Life run