This web site will let you interactively play the (k,ℓ)-pebble game algorithm. In the main area below, you should see two panes: an input pane and a game pane.

• Changing the parameters k and ℓ through the fields above will reset the game.
• (Un)check the "Auto-advance" option to toggle whether the game pane should show the latest game board.
• Use the 彡☆ button to complete the game by attempting to insert any remaining edges.

Input graph pane options

• selection 🅂 mode lets you select edges. If an edge has not yet been considered for the game, clicking the edge will attempt to insert it. If the edge was rejected already, clicking it will highlight its associated circuit (minimal dependent set for which dropping any element will regain sparsity).
  If you click on empty space, you can pan the view. If you click on a vertex, you can change its position.
• connect 🄲 mode lets you add edges. To add an edge, click to (un)select first vertex; click the second vertex to connect.
• add 🄰 mode lets you add vertices. Click on blank space to add a new vertex.
• deletion 🄳 mode lets you delete vertices/edges. If you delete a vertex/edge, all rejected edges are reset since there is a possibility that they could now be added to the game board. If you delete a vertex/edge while on an intermediate frame, all remaining frames will be removed. Use the 彡☆ button to complete the game (or click edges indvidually).
• Use the print tool to output a JSON string of the framework to the area below.
• Use the clear tool to remove the framework.