Deborah R. Fowler

Squares Illusion (Modulus)

Posted Dec 27 2019 Updated Dec 8 2020 animation; Update June 22 2023 3D anim Updated March 18 2026


Also on youtube at https://www.youtube.com/watch?v=wKpmDf5EYq8


Continuing with Illusions, from https://www.rd.com/article/optical-illusions/ I thought this looked like an excellent example to display modulus. Modulus is the remainder on integer division and made the recreation of this illusion easier to reproduce in Houdini.
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As seen below, this illusion is using modulus.
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To start, create a rectangle using an add node. Clip node by 45 degrees on each end. Use modulus to apply black to every other clipped rectangle. Copy that triangle to create a larger triangle
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Copy the compliment. Using modulus with source grid points, select every other point, sort, and then every other point again. Do this for both patterns.
Below is the node network:
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Below is an animation of levels of "stripes".

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Taking this one step further, copy these faces onto the points of a cube to get a 3D version. The box faces are scaled to zero in the primitive node and the points fused. The settings for the fuse node are below.

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Added June 23, 2023 a 3D animation from January



Also on https://www.youtube.com/shorts/CTqtFjv1PO4