The simulator visually generates every cyclic rotation of an input string, sorts them lexicographically to build the Burrows-Wheeler Matrix, highlights the resulting last column as the transform output, and then walks step by step through the reversal process using the first-column, last-column relationship to rebuild the original string.
Type or select a sample string, then step through rotation generation to see all cyclic shifts appear, trigger the sort to watch the matrix reorder alphabetically, observe the highlighted last column as the transform, and finally press play on the reversal animation to see the original string reconstructed one character at a time using only the transform and the origin index.
Text input field for the source string, step buttons for generate rotations, sort rotations, and extract last column, a toggle to show or hide the full rotation matrix, a play and step control for the reversal animation, and a reset button to load a new example string.
Did you know that the same last-to-first column relationship that lets you undo the Burrows-Wheeler Transform also powers near-instant DNA sequence search? The FM-index used by genome aligners like BWA reuses this exact mapping, just to narrow down matching positions instead of reconstructing a string, allowing billions of DNA bases to be searched almost as fast as reading the query itself.
The simulator visually generates every cyclic rotation of an input string, sorts them lexicographically to build the Burrows-Wheeler Matrix, highlights the resulting last column as the transform output, and then walks step by step through the reversal process using the first-column, last-column relationship to rebuild the original string.
The simulator visually generates every cyclic rotation of an input string, sorts them lexicographically to build the Burrows-Wheeler Matrix, highlights the resulting last column as the transform output, and then walks step by step through the reversal process using the first-column, last-column relationship to rebuild the original string.
Type or select a sample string, then step through rotation generation to see all cyclic shifts appear, trigger the sort to watch the matrix reorder alphabetically, observe the highlighted last column as the transform, and finally press play on the reversal animation to see the original string reconstructed one character at a time using only the transform and the origin index.
Did you know that the same last-to-first column relationship that lets you undo the Burrows-Wheeler Transform also powers near-instant DNA sequence search? The FM-index used by genome aligners like BWA reuses this exact mapping, just to narrow down matching positions instead of reconstructing a string, allowing billions of DNA bases to be searched almost as fast as reading the query itself.