Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

The magic eye optical illusions create stereographic pictures by taking two rectangles and slightly shifting the patterns, so that when you cross your eyes to overlap them, the subtle differences correspond to height.

This motivates my question: given a continuous function $f$ from the unit square to the interval $[-\delta,\delta]$ for some small $\delta$ (say, .01), do there exist functions $g_1,g_2$ from the unit square to the left and right open half spaces, respectively, of the Euclidean plane, such that:

  • Each $g_i$ preserves $y$-coordinates, and
  • The distance between the $x$-coordinates of $g_1(x_0,y_0)$ and $g_2(x_0,y_0)$ is $3+f(x_0,y_0)$, and
  • Each $g_i$ is within $\delta$ of a translation of the square, using the $\sup$ norm for continuous functions?
share|improve this question
add comment

1 Answer 1

up vote 2 down vote accepted

Yes. For example $g_2(x,y)=(x+1+\frac{1}{2}f(x,y),y)$ and $g_1(x,y)=(x-2-\frac{1}{2}f(x,y),y)$.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.