Leaf Surface Function in Three Variables

A few nights ago, I spent around 3 hours (probably more) drawing graphs of three dimensional surfaces for my multi-variable calculus homework. Since I can’t draw, this was going rather badly. Gradually, however, I realized that if I drew the function at multiple levels and then connected them with lines leading to a vanishing point, it was vaguely possible to tell that my surfaces were three dimensional.

The next day, I went into the Crum, thinking I should really do a sketch this week, since I’ve been avoiding it up until now. Suddenly, I walked past a large patch of plants with large leaves. Staring at the veins, I was powerfully reminded of the surfaces I’d been drawing the night before. Maybe if I used the same technique, they would turn out to look like something other than vaguely circular looking blobs – the normal result of my attempts to draw leaves. So I gave it a shot. It’s not perfect, but I’m really happy with how it turned out, compared to most of my drawings.

My sketch of the leaf

Graph of 4*x^2*(x^2+y^2+z^2+z)+y^2*(y^2+z^2-1) = 0 (function that the leaf resembles)

Photograph of actual leaf

(this function isn’t a great approximation, but it’s the best one I could come up with)

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