koch.js

let deg = Math.PI/180;  // For converting degrees to radians

// Draw a level-n Koch snowflake fractal on the canvas context c,
// with lower-left corner at (x,y) and side length len.
function snowflake(c, n, x, y, len) {
    c.save();           // Save current transformation
    c.translate(x,y);   // Translate origin to starting point
    c.moveTo(0,0);      // Begin a new subpath at the new origin
    leg(n);             // Draw the first leg of the snowflake
    c.rotate(-120*deg); // Now rotate 120 degrees counterclockwise
    leg(n);             // Draw the second leg
    c.rotate(-120*deg); // Rotate again
    leg(n);             // Draw the final leg
    c.closePath();      // Close the subpath
    c.restore();        // And restore original transformation

    // Draw a single leg of a level-n Koch snowflake.
    // This function leaves the current point at the end of the leg it has
    // drawn and translates the coordinate system so the current point is (0,0).
    // This means you can easily call rotate() after drawing a leg.
    function leg(n) {
        c.save();               // Save the current transformation
        if (n === 0) {          // Nonrecursive case:
            c.lineTo(len, 0);   //   Just draw a horizontal line
        }                       //                                       _  _
        else {                  // Recursive case: draw 4 sub-legs like:  \/
            c.scale(1/3,1/3);   // Sub-legs are 1/3 the size of this leg
            leg(n-1);           // Recurse for the first sub-leg
            c.rotate(60*deg);   // Turn 60 degrees clockwise
            leg(n-1);           // Second sub-leg
            c.rotate(-120*deg); // Rotate 120 degrees back
            leg(n-1);           // Third sub-leg
            c.rotate(60*deg);   // Rotate back to our original heading
            leg(n-1);           // Final sub-leg
        }
        c.restore();            // Restore the transformation
        c.translate(len, 0);    // But translate to make end of leg (0,0)
    }
}

let c = document.querySelector("canvas").getContext("2d");
snowflake(c, 0, 25, 125, 125);  // A level-0 snowflake is a triangle
snowflake(c, 1, 175, 125, 125); // A level-1 snowflake is a 6-sided star
snowflake(c, 2, 325, 125, 125); // etc.
snowflake(c, 3, 475, 125, 125);
snowflake(c, 4, 625, 125, 125); // A level-4 snowflake looks like a snowflake!
c.stroke();                     // Stroke this very complicated path