Deborah R. Fowler
Spiral Illusion - Exponential Growth
Posted Dec 23 2019
Updated Dec 27 2019
Exponential Growth is defined as "growth whose rate becomes ever more rapid in proportion to the growing total number or size". This plays a large part in the solution to the "Spiral Illusion".
Inspiration REFERENCE by Akiyoshi Kitaoka, this spiral illusion which is concentric circles that appear to be spirals can be found at http://www.ritsumei.ac.jp/~akitaoka/uzu-e.html.
I recreated this pattern in Houdini. On the right is my RESULT. The illusion is named "Kame wa mannen" (Turtles live long). This also includes a link to a paper talking about spiral illusions. (https://www.ncbi.nlm.nih.gov/pubmed/11430247?dopt=Abstract)
Continuing with Illusions, this is a good exercise in problem solving and is similar to the Line Illusion, Bend line Illusion, and Autumn Illusion. Problem solving is a necessary skill. How would you approach this? I will walk through my approach below.
Looking at the image, it was clear the circles were growing exponentially. The solution that looked visually correct was resolved by using an exponential curve with the expression in Houdini: pow(1.2,$CY)
A graph of this function looks as follows:
The other important factor is to rotate each concentric circle 10 degrees.
In order to obtain the normal to the circle to orient the objects copied to the circle correctly I have used a tube, reduced it to points and deleted one face. This could also be done with a circle and then a polyframe node to obtain the normal and up information.
Here are some variations on this pattern:
To break the illusion, we can follow the concentric circles as seen below (middle pattern above with green concentric circles traced and another version of the first image):
A similar illusion is described on wikipedia as a Fraser spiral illusion (first described by British psychologist Sir James Fraser in 1908).
Below is the wikipedia image and my version in Houdini using the same techniques as the one above.
The illusion can be more easily seen when the circles are identified.
Another inspiration, again replicated using the same technique was found at https://creativemarket.com/Tartila/3852215-Optical-spiral-illusion.-Magic
and can be found at https://www.123rf.com/photo_122571185_stock-vector-optical-spiral-illusion-magic-psychedelic-pattern-swirl-illusions-and-hypnotic-abstract-background-a.html
I created the following in Houdini:
The illusion is revealed in the animation
And Finally, a few variations, again using this technique:
Below, there is no rotation of the object, just a camera move toward the object and ...
... the second version away from the object
A few more - the last two animating the rotation - note that the third row from the outside appears to not rotate in the gif below, however the red dot shows it is indeed rotating.
Subtle changes in the orientation of the object affect the pattern as seen by these side-by-side
