Level 5-6
Parametric Pinball
Navigate parametric paths — cycloids, Lissajous figures, and spirals — to reach the goal!
0 /30 Stars
0 /10 Tasks
Tasks
Adjust parametric sliders to guide the marble along cycloids and Lissajous curves. Earn up to 3 stars per task — unlock the next by completing the previous!
This is a cycloid — the mathematically optimal slide. Set a = 1. Watch the marble ride the arch and reach the next cusp. Task 1
Marble Increase 'a' to scale the cycloid. Find the value that places the arch's lowest point on the goal. Task 2
Marble A large 'a' creates a wide, low arch. Route the marble across the long arch to the goal at the far right. Task 3
Marble Set a < 1 to compress the cycloid into tight, rapid loops. The goal is close — find the right scale. Task 4
Marble The goal is at the lowest point of the first arch, not at a cusp. Adjust 'a' so the arch's trough lines up with the goal. Task 5
Marble The track is a Lissajous figure. Adjust a and b so the marble follows a path through the goal. Task 6
Marble Change the integer ratio a:b to produce a different Lissajous knot. Find the ratio that crosses through the goal. Task 7
Marble Set n = 3 to create a three-loop Lissajous figure. One of the loops passes through the goal — steer the marble into it. Task 8
Marble A high n creates many small loops. Adjust a and b so one loop encircles the goal zone. Task 9
Marble The ultimate challenge: all sliders active. Design a parametric path that threads the marble into the smallest goal of the entire game. Task 10
Marble Start with Cycloid Basics to learn how the marble follows a parametric path, then progress through scaled cycloids and Lissajous figures. The final Grand Parametric Finale combines everything you've learned!
Tip: In a cycloid, the parameter a controls the size of each arch. In Lissajous figures, the ratio a:b determines the shape — try integer ratios for clean loops.