Klotho spins the thread of life, Lakhesis measures it, Atropos cuts it short - the Moirai
lakhesis is a rust implementation of the sandpile model on a rectangular lattice that seeks to explore the interaction between two or more sandpiles. In this implementation of the sandpile model grains of sand fall onto a surface, imagined here as a square table, which accumulate to a height of three grains per cell. Adding a fourth grain causes the pile to topple and sends the grains to the four adjacent cells. If these adjacent sand grain piles exceed three grains, they will in turn also tumble and send sand grains to their neighbors, possibly causing an 'avalanche' of tumbling piles. Sand grains reaching the edge of the table will 'fall off' and are considered lost. The model has been used to study self-organizing criticality.
I noticed that adding a second sand pile resulted in interesting, and recurring, patterns at the boundary between the two piles. Lakhesis has been set up in order to explore how these boundary patterns develop and how factors such as the number of additional piles and their orientation and distance from each other affect these patterns. The lattice is set to 3,000 by 3,000 pixels, large enough to contain a single sandpile of approximately 16 million sand grains or an equivalent number distributed between multiple sandpiles. The color of cells with three grains is set to transparent black in order to emphasis the patterns that cross through these stable areas. Many of these patterns have the appearance of threads intertwining and weaving into textile-like surfaces (i.e. the name of the project - apologies for the mixed metaphors).
Check out a wasm version that runs in your web browser - give it a few seconds to load
Sandpile model, Cellular automaton, Self-organized criticality, Rust, Macroquad
lakhesis was compiled using rust 1.63.0
macroquad
cargo run --releaseThere are no command line arguments. Menu and keyboard commands are available after execution starts and are shown in an information box at the top left corner of screen. Yellow text in the "Info" box provides rudimentary context-based instructions.
- [A] Add a new sandpile to the simulation. Add up to a maximum of 32 sandpiles.
- [C] Change the colors displayed with a randomly selected new set of colors.
- [I] Bring up the info panel if its hidden. Hide the panel if its visible.
- [M] Magnify a 32 by 32 pixel square by a factor of 4. Use mouse to select location.
- [P] Pause the simulation. Press [P] again to resume simulation.
- [S] Save an image of the lattice as a PNG. The file is saved to the project folder.
- [Spacebar] Step through the simulation one interval each time the [Spacebar] is pressed.
- [Up] The up arrow increases the interval between screen updates by a factor of 4 to a maximum of 16,384.
- [Down] The down arrow decreases the interval between screen updates by a factor of 4 to a minimum of 1.
- [CTRL-N] Starts a new simulation - not shown on the
wasmversion. Use the browser's reload command.
The macroquad game engine can be compiled to run on web browsers - directions
Before compiling lakhesis for wasm it is suggested that the IO_SUPPORTED constant in "lui.rs" be set to "false". This will remove some features that are not supported in web browsers.
rust provides a local server that can be used to host the webpage on your system. After following the macroquad directions to create a wasm file and copying/editing the provided "index.html" and "mq-js-bundle.js" files into the same folder as the wasm file open a terminal in that project folder and install basic-http-server:
cargo install basic-http-server
basic-http-serverResponse time to keyboard commands and mouse movement will get sluggish as the sandpile grows. The simulation has its own crosshairs which follow the mouse cursor around. The lag between mouse and crosshair movement will give you an indication of how long the algorithm is taking to process the addition of new sand grains. Try reducing the "Interval" [Down Arrow] to improve responsiveness. Areas of the lattice outside the screen view can be reached using direction buttons in the menu. The center 'O' button will re-center the window over the midpoint in the lattice when the screen is refreshed.
When the simulation starts a gray dot indicates the centerpoint of the 3,000 by 3,000 lattice so that a new sandpile can be started in the exact middle of the lattice, if desired. The point is just a guide - new sandpiles can be started anywhere within the lattice. If the model is run with only one sandpile, it will generate the standard sandpile image seen at the top of this page. Adding additional sandpiles will generate images similar to the second image above. A menu option of pressing the [C] key will allow you to change the colors used the by model. Generating new colors doesn't impact any other aspect of the model and they can be repeatedly changed, however values of the old colors are not saved.
This version of lakhesis replaces the blue menu window with a macroquad user interface that includes buttons to alter the configuration of the simulation and information on the model. Most keyboard commands are still available and the menu can be hidden from view. When Lakhesis starts it defaults to refreshing the screen every 1024 interations (an interval of 1024 sand grains that have been added to the model). The display interval can be changed by a factor of 4 down to a minumum of 1 (refreshing the screen for each sand grain added) and up to a maximum of 16,384. Initially, more frequent screen updates slow down overall progress of the model, however the interesting patterns mentioned above are more apparent at smaller intervals. Conversely, increasing the interval between updates can 'speed' up the model to get to the point where the edges of sandpiles interact, at which point the interval can be decreased to observe the interference patterns. As the number of sand grains becomes substantial the simulation will become less responsive as more time is needed to evaluate the model. At this point the time needed to refresh the screen is inconsequential compared to the evaluation time and the interval should be reduced to make the model more responsive to keyboard commands. When frames per second (FPS) drops to 0, the "Current Frame Time" and "Average Frame Time" variables can help estimate how long it will be till the next screen update. Average frame times generally increase as the sandpiles grow in size, however the difference between consecutive frame times can be substantial. For example, one long frame time might be followed by serveral short ones.
The biggest change in this version is the addition of a color menu that allows control of every color combination, including the background, through the use of macroquad ui slider-bars for the red, blue, green, and alpha channels. An option to randomly generate colors remains. There are two undocumented features. One is a very experimental option to save the model to a text file by pressing the [G] key and retrieve a saved simulation with [CTRL][H]. The saved file will be named 'lakhesis_nnnnnn.lak' where nnnnnn is the total number of sand grains present. The retrieved file must be named 'lakhesis.lak'. Pressing [CTRL-V] will export a large number of PNG images at the set interval. [V] stands for video, however the command doesn't actually create a video, rather it exports an image of the visible portion of the model at a constant interval. The number of images is set to 600 by the constant VIDEO_FRAME_COUNT in "main.rs". These 600 images could, for example, be animated with video editing software to produce a 10 second video at 60fps. WARNING - using the video command will dump 600 images in your project folder. Pressing [ESC] will cancel the command. The [S]napshot command works a little differently - it exports a PNG image of the active portion of the entire lattice with a 10-pixel blank boundary around the edges - even if the whole image is not visible on the screen. The boundary and the 'black' triangular areas in the image default to transparent and can be easily manipulated with image editing software or the background color and transparency can be altered in the color menu.
lakhesis build is failing on github with error "/usr/bin/ld: cannot find -lasound", but does build on my ubuntu 22.04 setup after installing:
# ubuntu system dependencies
apt install pkg-config libx11-dev libxi-dev libgl1-mesa-dev libasound2-dev
# fedora system dependencies
dnf install libX11-devel libXi-devel mesa-libGL-devel alsa-lib-devel
# arch linux system dependencies
pacman -S pkg-config libx11 libxi mesa-libgl alsa-libMy contact info is in the "cargo.toml" file.
The content of this repository is licensed under Apache License 2.0