Stop Motion (Triangle Tree)

The Digital Flip-Book

For this experiment, I took inspiration from the Pythagorean Tree, a mathematical design based upon recurring geometric shapes that adhere to Pythagoras' theory. Pythagoras theory named after the Greek philosopher and mathematician and founder of the Pythagorean Brotherhood (Brittanica, 2024), maintains that the square root of a right-angled triangle’s hypotenuse is equal to the sum of the square roots of the opposite two sides a2 + b2 = c2. The Pythagorean tree construction demonstrates proof of the mathematical theory, the first known drawing of the tree was created by Dutch electrical engineer and mathematics teacher Albert E. Bosman (1891-1961) in approximately 1942 (Riddle, n.d.).

Example Pythagorean Tree.

For the experiment, I wanted to create a Pythagorean Tree or something that resembled one, that grows from a planted triangular seed. My concept was to combine inorganic geometric shapes into an organic structure. My expectation was that the short video (or long GIF) would be fun rather than hold any educational value.

I used the timeline feature of Adobe Photoshop to create the graphics, applying each new movement to a separate layer. The triangles were created using Photoshop’s  Triangle Tool which whilst useful for creating triangles was very limited when trying to maintain a right-angled triangle or manipulating the triangle to fit it into place on the tree. In addition to the triangle tool, I needed to use the Free Transform and Transform/Rotate tools to position each object. As a result, the process was extremely time-consuming.

Photoshop’s Timeline feature requires the running time for each layer and the timing between each layer to be manually adjusted. The timeline presents each layer separately, reminiscent of their Premier Pro or Premier Rush applications. When it is first opened, all layers are stacked one on top of the other. The timeline and video are created by pulling each of the layers along the timeline as shown in the diagram below:

The finished animation was not particularly appealing and rather too slow to be considered a flip-book. I opened the MP4 file that Photoshop had created, into Premier Rush where I condensed the timeline to make each transition shorter, I also added sound effects from Premier Rush’s library of license-free media. The result following the Premier Rush edits was far better. The finished work sits somewhere between a short video and a long GIF.

I decided to make a GIF out of the MP4 file, in order to do so I loaded the video file into Adobe Premier Pro and exported it as a .GIF file.

The video file, which includes the soundtrack and improved resolution can be seen here: https://youtube.com/shorts/Hx4Bd2OIir4

BRITTANICA, 2024. Pythagoras | Greek philosopher and mathematician [Viewed 03/11/2024]. Available from: https://www.britannica.com/biography/Pythagoras

RIDDLE, L., Pythagorean Tree [Viewed 03/11/2024]. Available from: https://larryriddle.agnesscott.org/ifs/pythagorean/pythTree.htm