These are grasshopper recreations of a design pattern 'Increment' found in Robert Woodbury's Elements of Parametric Design. Variations of spirals are created and are controlled by sliders (definition 1) and graph mappers (defintion 2).
In both definitions points are plotted with the coordinates ( r * cos(theta), r * sin(theta), z). An interpolated curve is fit through the points resulting in spiral-like curves. The increments in theta, r and z values are controlled differently in both definitions in order to produce variations in the curve.
In the first definition, the z and theta variables are incremented linearly using a 'series' component, while r is held constant. This results in points that are constrained to the surface of a cylinder.
In the second definition, z variable is increased linearly, but both increments in theta and r variables are controlled by graph mappers. Graph mappers allow for more precise and varied control over a series of values. Feed a 'range' into the Graph mapper component,select a default graph type and a series of values will be output based on the selection.
The grasshopper definitions can be downloaded here.
Videos of Increment 1 and 2: