by dennedesigns, published

Octopus by dennedesigns Mar 31, 2016
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175Views 77Downloads Found in Math Art


This toy octopus was designed by DanJoesph Quijada and edited by Dave Pfaff and myself in my Math 341 Introduction to Topology class in Fall 2014. The shape of the legs is based on a sinusoidal curve which decreases exponentially with each oscillation.

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You may need to rescale this object by a factor of 10 in Makerware since it is sized in cm not mm. You may also need to move the knot onto the platform, I think it is just above it. The octopus is about 12cm x 12cm x 4cm in size. I ended up printing it so the legs were about 10cm x 10cm in size. This model was first printed on a Project 260 3D Systems printer.

When I first printed this model on standard settings for the MakerBot 2X, a couple of legs had noticeable jumps in them and the head was kind of lumpy where the plastic had cooled unevenly. I fixed this by printing the model mostly solid (80% infill), also by changing the support angle from the standard 68 degree to 45 degrees.

How I Designed This

This model was designed entirely in Cinema4D. The legs were made using parametric equations like x(t) = a\sqrt{2}t, y(t)=0, z(t) = b^2 cos^2(ct)e^{-dt^2} for various constants a, b, c, and d, and bounded time t. These curves were then thickened using a SweepNurbs. To make the octopus head, we first made a box, then extruded parts of the sides to alter the shape, then applied HyperNURBS to it. Finally we made minor adjustments, such
as adding the eyes and changing the dimensions of the octopus to make it
look more realistic.

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