This video explores a captivating optical illusion where spinning objects, particularly those exhibiting natural growth patterns based on the golden ratio (phyllotaxis), appear to shrink or grow when viewed through a camera or with a synchronized strobe light.
The phenomenon is explained as a form of "3D zoetrope," where the camera's frame rate or the strobe's flash frequency aligns with the object's rotation. The key lies in the "golden angle" (360 degrees divided by the golden ratio, approximately 222 degrees), which governs the arrangement of elements like seeds or petals in many plants. When rotated by this specific angle per frame/flash, each successive element subtly shifts position, creating the illusion of continuous outward "growth" or inward "shrinking." The irrationality of the golden angle allows for an infinite number of unique animation speeds, unlike traditional zoetropes.
The creator demonstrates this with various natural objects (cacti, pine cones) and custom 3D-printed models designed using Onshape CAD software. An interactive website is also introduced for users to experiment with the parameters. Finally, the video showcases the "Novatropes" device, a commercial product that uses a synchronized strobe light and precise motor control (derived from CD players with IR feedback) to make this fascinating illusion visible to the naked eye.
Summarizing the Golden Ratio in Motion: The Shrinking/Growing Cactus Illusion
0:00 The Spinning Illusion: The video introduces a captivating optical illusion where spinning objects like cacti, pine cones, and succulents appear to shrink or grow when filmed with a camera, an effect dependent on the camera's shutter speed.
0:31 Zoetrope Explained: This phenomenon is a form of a zoetrope. Traditional zoetropes use slits to flash images, creating an animation. Here, the camera's frame rate (or a strobe light for naked-eye viewing) acts similarly, capturing a new "frame" of the spinning object.
1:37 Nature's Mathematical Pattern: The illusion works particularly well with objects exhibiting phyllotaxis, a natural growth pattern found in many plants. The video uses a 3D-printed flower to demonstrate this "geometrically perfect" pattern.
2:12 The Golden Angle: Plants generate new elements (seeds, petals) by turning through a specific angle between each one. For the most efficient use of space, this angle is the "golden angle" – a full circle (360°) divided by the golden ratio (approximately 222°).
3:38 Animation Without Golden Ratio: The creator demonstrates that while the golden ratio makes the effect "better," animation can still occur with other patterns, like a 5-spoked plant designed with a 2/5ths turn between petals.
4:17 Onshape CAD & Parametric Design: The creator uses Onshape, a cloud-based CAD system (sponsor), to design parametric models, allowing easy adjustment of the angle between petals to observe different spiral patterns, including the golden ratio spiral.
5:48 Interactive Website: An interactive website is shared, enabling viewers to experiment with frame rate and the angle of rotation between elements to understand how the animation works.
6:05 Explaining Shrinking/Growing: The illusion occurs because when the object rotates by the golden angle (or a multiple thereof) between camera frames, each seed/petal appears to have drifted slightly outwards or inwards, creating the perception of growth or shrinkage.
7:33 Infinite Speed Options: The irrationality of the golden angle means that rotating an object by this angle will never return it to its exact original position, resulting in an infinite number of unique animation speed options, unlike standard zoetropes.
8:36 Every Element Visible: A remarkable feature of golden ratio-based animations is that if you fix your gaze on one point, every single seed, spike, or petal of the plant will eventually visit that exact location.
9:05 Novatropes for Naked Eye Viewing: The "Novatropes" device by Brendan Keeber is introduced as a way to experience this illusion without a camera. It uses a synchronized strobe light (flashing around 40Hz) and a spinning base (driven by a CD player motor with an infrared sensor for speed control) to make the effect visible to the naked eye.
10:25 Custom STL Available: The creator makes their channel logo design available as an STL file for anyone who owns a Novatropes device.