Experiments with a helix, including varying the radius, shifting the center, and varying the number and spacing of turns.

ParametricPlot3D[ { 2 * Cos[6*Pi*t] + 1, 3*Sin[6 * Pi* t], 0.5 * t }, {t,0, 1}]

A particularly interesting curve someone created by scaling the arguments to sine and cosine differently in a helix.

ParametricPlot3D[ { 2 * Cos[6*Pi*t] + 1, 3*Sin[ Pi* t], 0.5 * t }, {t,0, 1}]

A conical helix.

ParametricPlot3D[ { t * Cos[6*Pi*t], t*Sin[6 * Pi* t], 0.5 * t }, {t,0, 1}]

The center line for the “snake.” Note the use of “PlotRange -> Full” to force Mathematica to show the plot over the full range of x, y, and z values.

ParametricPlot3D[ { t, Sqrt[t]*Cos[4*Pi*t],t^20}, {t,0,1},PlotRange->Full]