Golden Spiral

I've always enjoyed drawing versions of the Golden or Fibonacci Spiral, generally starting with a rectangle twice as long as it is wide, then guesstimating the halfway points as I alternated cutting the rectangle in half horizontally and vertically, always moving in towards the center. As each segment of the rectangle is squared downwards, the vertices of each segment could be connected with a spiral growing outwards from the smallest point that could be drawn.

This SVG file is the same representation, just done with hand-coding and a little more math than my original sketches. The largest outer rectangle is cut in half horizontally, then the upper portion is cut in half vertically, then the upper-right portion is cut in half horizontally, the lower portion of that is then cut in half vertically, and so on and so forth. Cubic curves are used to create the spiral, with the control points set to the halfway points of each starting and ending edge of the current segment.

So starting from the lower-right corner of the rectangle, the first control point of the curve is set to the halfway point along the bottom edge of the rectangle while staying at the same Y value as the starting point, and the ending control point is set to the halfway point between the lower-left corner and the horizontal cut point which is where the ending point is set. This pattern of putting the control points on the halfway parts of their corresponding edges allows for a smooth spiraling curve to develop the deeper into the drawing we get.

Download the Golden Spiral SVG file

A large rectangle twice as tall as it is wide. The rectangle is halved horizontally with a line, the upper portion is halved vertically, and the halving pattern continues in a clockwise direction growing smaller as each segment nears the center of the rectangle. A red smooth spiral emanates outwards from the smallest set of cuts, connecting each vertex all the way out to the outer-most rectangle edges.