Back in the day, the only tools available were compass and straightedge. A technique they used still works quite well in the digital age. The simplest method, traditionally using only a compass, is a two point spiral.
The other method used both compass and straightedge. Polygons and lines are used as the basis. The “points” in this instance will be those at the vertices of the polygon.
The first example will use a triangle which creates a 3 point spiral. The appearance is somewhat more balanced than the previous 2 point spiral.
Construction is similar to the 2 point method. Instead of alternating between two points, the center of each successive circle is the next vertex of the triangle. Each new circle is tangent to the previous circle where the common radius lines are parallel. The progression of circles continues until the desired diameter is achieved.
Trimming involves removing 2/3 of each drawn circle. Starting adjacent to the first tangent point as shown. Continue with the remaining circles and construction lines. The initial circle is a tighter radius in proportion to the rest and it’s line may be removed.
Trimming of earlier circles may also be accomplished as each new circle is drawn instead. If while drawing you get “lost”, merely tap the prior circle to show which vertex the next origin is to be placed on.
I have drawn multiple point spirals and have found the 6 point to be the most visually appealing. Construction is identical the the three point. Though 5/6 ths of each circle is trimmed at the finish. Note the distance between spiral lines is 6 times the length of one side of the initial hexagon.
