https://github.com/ratwolfzero/hopalong
"Hopalong attractor" calculate, display and save as image
https://github.com/ratwolfzero/hopalong
attractors fractals hopalong rust-lang strange-attractors
Last synced: 24 days ago
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"Hopalong attractor" calculate, display and save as image
- Host: GitHub
- URL: https://github.com/ratwolfzero/hopalong
- Owner: ratwolfzero
- Created: 2023-09-30T19:27:25.000Z (over 1 year ago)
- Default Branch: master
- Last Pushed: 2024-08-29T00:31:02.000Z (8 months ago)
- Last Synced: 2024-08-29T01:37:01.345Z (8 months ago)
- Topics: attractors, fractals, hopalong, rust-lang, strange-attractors
- Language: Rust
- Homepage:
- Size: 2.31 MB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# hopalong
## Abstract
### Historical Context
The "*Hopalong*"* attractor, authored by Barry Martin of Aston University in Birmingham, England [2], was popularized by A.K. Dewdney in the September 1986 issue of *Scientific American*. In Germany, it gained further recognition through a translation titled "*HÜPFER*" in *Spektrum der Wissenschaft* [3].
*Nicknamed by A.K. Dewdney.
### The Hopalong Attractor Functions
This Rust program computes and visualizes the “hopalong” attractor by iterating the following system of recursive functions:
$$
\large
\begin{cases}
x_{n+1} = y_n - \text{sgn}(x_n) \sqrt{\lvert b x_n - c \rvert} \\
y_{n+1} = a - x_n
\end{cases}
\large
$$
Where:
- The sequence starts from the initial point (x0 , y0) = (0 , 0)
- xn and yn represent the coordinates at the n-th iteration
- a, b, and c are parameters influencing the attractor's dynamics
- *sgn* is the *signum* function
### Features and Further Information
The color scheme is based on the pixel density, i.e. how often a pixel of the image is hit during the iteration.
For more information in general and about “pixel density”, i.e. displaying the attractor as a density heatmap, see my Python versions repository.
For information on the implementation of the Signum function in Rust, see:
You can run this program from the command line in a terminal.
The number of iterations (num) can be entered as integer or in exponential form such as 1e6.
Example: ./hopalong -2 -0.33 0.01 2e8 (MacOS)
If you are using a Mac with Apple Silicon you should be able to use the executable in the 'Binary' folder.
The binary was compiled on a Mac Mini with M2 processor.
The calculated image should be displayed but there will be an error regarding saving the image.
// Save the image with the generated name
let save_path = format!("/Users/ralf//Projects/hopalong_pictures/{}", image_name); // Specify your desired save path
if let Err(e) = image_buffer.save_with_format(&save_path, ImageFormat::Png) {
eprintln!("Error saving image: {}", e);
} else {
println!("Image saved to: {}", save_path);
}
----------------------------------------------------------------------------------------------------------------------------------------------------
## References
[1]
**J. Lansdown and R. A. Earnshaw (eds.)**, *Computers in Art, Design and Animation*.
New York: Springer-Verlag, 1989.
e-ISBN-13: 978-1-4612-4538-4.
[2]
**Barry Martin**, "Graphic Potential of Recursive Functions," in *Computers in Art, Design and Animation* [1],
pp. 109–129.
[3]
**A.K. Dewdney**, Program "HÜPFER," in *Spektrum der Wissenschaft: Computer Kurzweil*.
Spektrum der Wissenschaft Verlagsgesellschaft mbH & Co., Heidelberg, 1988.
(German version of *Scientific American*).
ISBN-10: 3922508502, ISBN-13: 978-3922508502.