The Math Behind

Yup performs extensive computation on the modified logistic equation and reveals the colorful interplay between chaos and order.

The article "Leaping into Lyapunov Space" , published in Scientific American in 1991, describes how dynamic systems can be turned into gorgeous images by the use of the Lyapunov exponent.

Zooming in

Zoom in the Lyapunov space and create your individual Yup image:
  • Tap settings
  • Tap on the row "X Value Range" or "Y Value Range"
  • Change position of the rectangular by dragging
  • Change rectangular size by dragging the left bottom corner
  • Hide/show tab and status bars by tapping the screen
  • Tap Done and then Compute
  • Experiment with different colors
  • Save the image in your camera roll

Color Wheel

Paint gorgeous Lyapunov spaces with the color wheel. Hue an saturation can also be set in landscape mode.