Sliceforms

I rather like making things. Sliceforms are just a neat way of representing a 3D surface with paper. It’s much easier just to show you pictures than to try and explain in words.

Cosinus

The cosinus sliceform

My first go was quite a nice surface, but I just used white paper and made no attempt to hide the construction lines. The form of the equation (without constants) was a decaying cosinus curve, satisfying

z = e − r cos ( θ ) z=func e^{-r}cos(%theta) ,
where r = ( x 2 + y 2 ) r=sqrt(x^2+y^2)

I unfortunately lost the pattern, so I never made a neat version.

Monkey Saddle

The monkey saddle sliceform

The next one I decided would be neater. This one is a ‘monkey saddle’, with the form

z = x ( x 2 − y 2 )

again ignoring constants (to tweak its shape so it looks nice). I do still have the pattern for this one.

(Those particularly astute readers may have noticed that this pattern has half the number of slices to the one in the photo, and that the one in the photo was printed without the numbers in the corners. The pattern here is a remake of the original slices, made with gnuplot.)