Nature’s Optical Illusion

Summary

This video explores the mesmerizing effect of spinning cacti, pine cones, and other natural patterns, revealing why they appear to grow or shrink when filmed. Using concepts from zoetropes and the golden angle derived from the golden ratio, the creator demonstrates how nature's spirals can be animated through rotation. The video combines 3D modeling, parametric design in Onshape, and strobe-light techniques to replicate this effect for the naked eye. Viewers learn about the mathematical patterns behind seed and petal arrangement, the impact of rotational speed, and innovative devices like Novatropes that make these animations tangible, bridging science, art, and technology in a visually stunning way.

Takeaways

• 🌵 Spinning objects like cacti, pine cones, and succulents can appear to grow or shrink depending on camera shutter speed.
• 📸 The effect is primarily visual and can be enhanced or recreated using cameras or strobe lights for the naked eye.
• 🎞️ The animation effect is related to the principles of a Zoetrope, where sequential frames create the illusion of motion.
• 🌀 3D zoetropes can be created without the traditional slitted drum by arranging models in a circle and syncing with a camera's frame rate.
• 🌸 The patterns seen in plants, such as seed arrangements, are often geometrically perfect and can be replicated using 3D printed models.
• 🔢 The most efficient angle for seed placement in plants is the golden angle, derived from dividing a circle by the golden ratio.
• 💡 The golden ratio is highly irrational, allowing infinite speed variations in animations without repeating positions, enhancing the visual effect.
• 🎨 Parametric design tools like Onshape allow manipulation of angles and patterns to experiment with animations and golden ratio spirals.
• 💻 Websites and software can let users explore different frame rates and angles to simulate the growing and shrinking visual effect.
• 💡 Novatropes devices use strobe lights and spinning objects to replicate this animation for the naked eye, using sensors to maintain precise speeds.
• 🔄 The golden ratio ensures all seeds or petals appear at every location over time, making natural animations visually pleasing and mathematically fascinating.
• 🥦 Fractal designs, like Romanesco broccoli, also exhibit similar self-repeating patterns that can be animated using these principles.

Q & A

Why does a spinning cactus appear to grow or shrink when filmed?

The illusion occurs due to the camera's frame rate interacting with the rotation of the cactus. Each frame captures the cactus in a slightly different position, making it appear as if it is growing or shrinking.

Does this effect only work with cacti?

No, it also works with other natural objects like pine cones, succulents, and even geometrically perfect artificial flowers.

What is a traditional Zoetrope and how does it work?

A traditional Zoetrope is a device with slits that show a sequence of images on the opposite side when spun, creating the illusion of motion as each slit reveals a new frame.

How can a 3D Zoetrope be made without the slits?

By arranging 3D models in a circular pattern and relying on a camera's frame rate, the spinning objects appear animated when captured in successive frames.

What is the golden angle and why is it important in plant growth?

The golden angle, approximately 137.5°, is derived from the golden ratio. It is the optimal angle between successive seeds or petals for the most efficient packing, minimizing gaps and maximizing exposure.

Is the golden ratio necessary for the spinning animation effect?

No, the animation can work with other angles, but the golden ratio creates more uniform coverage and an aesthetically pleasing spiral, making the effect smoother.

How does changing the rotation angle between frames affect the animation?

Altering the angle can make the spiral appear to rotate, shrink, or grow. Multiples of the golden angle allow for different speeds while maintaining the illusion.

Why does the golden angle offer infinite speed options for animation?

Because the golden ratio is an irrational number, turning through multiples of the golden angle never perfectly aligns with the starting point, allowing infinitely varied frames and speeds.

How can the spinning effect be seen with the naked eye instead of a camera?

By using a strobe light or LED ring flashing at a precise frequency, the object is illuminated at intervals that mimic the frame-by-frame capture, creating the visual effect for the human eye.

What is the function of the infrared sensor in the Novatropes device?

The infrared sensor detects the position of the spokes as they pass, providing feedback to maintain the correct rotational speed for the strobe effect.

What software is recommended for designing 3D models like the spinning plant animations?

OnShape, a professional cloud-based CAD system, is recommended for parametric design, collaborative editing, and efficient 3D modeling.

Can you explain why the pattern in plants resembles a pentagram?

When a plant turns through certain angles between seed or petal placement, such as 2/5 of a full turn, the seeds align in a pentagram-like pattern, although this is less efficient than using the golden angle.