When I was young my parents bought me a Spirograph set at the flea market. I wasted lots and lots of paper with it. A modern treefriendly rendition:

Manipulate[ Module[{ (* noninteger values of \[Zeta] give progressively more entwined paths, but require smaller cycle widths to keep the plot from looking scrambled *) \[Psi] = Round[Abs[FractionalPart[\[Zeta]]]*1., .25] /. { 0. > y, .5 > y/2, .25  .75 > y/4}}, ParametricPlot[ (1. + spirality*(Log[\[Theta] + 1.]  1.))* {\[Psi] Cos[\[Theta]] + x Cos[64. \[Theta]] + (1  effect*RandomReal[])*\[Zeta]* (Cos[512. \[Theta]] + Cos[64. \[Zeta] \[Theta]]), \[Psi] Sin[\[Theta]]  x Sin[64. \[Theta]] + (1  effect*RandomReal[])* inflection*\[Zeta]* (Sin[512. \[Theta]] + Sin[64. \[Zeta] \[Theta]])} , {\[Theta], 0, 2 \[Pi]}, ImageSize > {470, 410}, PerformanceGoal > "Quality", (* reduced opacity helps bring the shape out and gives an elegant tone *) PlotStyle > {{color, Opacity[.43], AbsoluteThickness[thickness]}}, PlotRange > Full, PlotPoints > 270,(* increase for higherresolution images *) Axes > None]], OpenerView[{"Style", Column[{ Control@{{color, Black, "line color"}, ColorSlider}, Column@{ (* these controls are smallerized for consistency *) Control@{{thickness, 0., "line thickness"}, 0, 20, Appearance > "Labeled", ImageSize > Small}, Control@{{effect, 0., "charcoal effect"}, 0, .25, Appearance > "Labeled", ImageSize > Small}}}]}], Row[{ Control@{{inflection, 1}, {1 > " concave ", 1 > " convex "}, Appearance > "Vertical"}, Spacer[30], Column@{ Control@{{\[Zeta], 2., "angularity"}, 7.5, 7.5, .5, Appearance > "Labeled", ImageSize > Small}, Control@{{x, 8., "tension"}, 0, 12, Appearance > "Labeled", ImageSize > Small}}, Column@{ Control@{{y, 2., "cycle width"}, 0, 2, ImageSize > Tiny}, Control[{{spirality, 0.}, 0, 1, ImageSize > Tiny}]} }], Alignment > Center, SynchronousUpdating > False, AppearanceElements > "ManipulateMenu", Bookmarks > { (* this bookmark assigns random values to the factors. I intentionally didn't make this feature rapidfireable *) "Random" :> ( color = RGBColor[RandomReal[], RandomReal[], RandomReal[]]; inflection = RandomChoice[{1, 1}]; (* effect, thickness, and spirality have distributions that make small values smaller and large values rarer [you mean "power law"  future version of myself]*) effect = .25*RandomReal[]^8; thickness = 10*RandomReal[]^8; spirality = RandomReal[]^3; If[spirality < .035, spirality = 0]; x = RandomReal[]*12; y = RandomReal[]*2; Module[{ (* +/ .5 are generally not interesting when x > 3 *) weights = If[x > 3, {.1, .03, .87}, {.1, .07, .83}]}, \[Zeta] = RandomChoice[{1, 1}]*RandomChoice[weights > {RandomReal[7.5], (* small chance to fall on nonintegral \[Zeta] *) RandomChoice[{0, .5, .5}],(* multiple .5 isn't a typo *) Round[RandomReal[{1, 7.5}], .5]}]]; ), "Rose" :> {thickness = 0, color = Red, effect = 0, inflection = 1, x = 0, y = 1.1343, spirality = 0, \[Zeta] = 3}, "Glyph" :> {thickness = 0, color = Black, effect = 0.198, inflection = 1, x = 5.2, y = 0., spirality = 0, \[Zeta] = 2}, "Mass Atomic" :> {thickness = 0, effect = 0, inflection = 1, x = 5.84, y = 0.412, spirality = 0, \[Zeta] = 4.2504}, "Jello" :> {thickness = 0, color = Red, effect = 0, inflection = 1, x = 12., y = 0.846, spirality = 1., \[Zeta] = 1.}, "Grim" :> {thickness = 3.35, color = Black, effect = 0.0675, inflection = 1, x = 8., y = 0.296, spirality = 1., \[Zeta] = 1.}, "Angelwings" :> {color = RGBColor[0.07693598840314336, 0.39046311131456474, 1], effect = 0, inflection = 1, spirality = 1.`, thickness = 0, x = 12, y = 0, \[Zeta] = 5.4946511679431715`}, "Rollers" :> {color = RGBColor[0.`, 0.`, 0.`], effect = 0.`, inflection = 1, spirality = 0.`, thickness = 0.`, x = 5.5`, y = 0.1`, \[Zeta] = 0.984032039033508`}, "Lifespark" :> {color = RGBColor[0.1026, .9878, .0201], effect = 0, inflection = 1, spirality = .0995, x = 3.2757, y = .2002, \[Zeta] = 5.5} } ]
I'm particularly proud of this program because it can produce a wide variety of images from just a few parameters. Though that's not an accident. A lot of finetuning and experimentation was involved. For the "Super Mario 64" to this program's "Super Mario," see my Cycowtron 4800 Deluxe.