Double Pendulum
A photographic experiment
A photographic experiment
The point of this experiment was to demonstrate & capture the underlying patterns and hidden beauty that exists in even the simplest of chaotic systems.
To that end, a device known as a double pendulum has been constructed and it's end point tracked through the use of a small LED light.
Normally, a pendulum has the characteristic of being a strongly deterministic and mathematically easy to understand device. It's path easily predictable/computable even when examined in non-idealized conditions that include friction and air resistence.
A double pendulum, which is essentially a pedulum attached to a pendulum, although equally mathematically predictable assuming ideal conditions, exchibits extraordinerily complex behavior in real world conditions, their patterns deviating strongly from the mathematically predicted one. As the pendulum(s) constantly reach equilibrium points and exchange momentum and energy, small differences in the ambient conditions or the construction of the device can send the second pendulum in a completely different path and direction than expected. The movement of the second pendulum becomes chaotic, and in fact is so sensitive to the initial/local condition that even when released from the exact same point it will commit to a different path every time.
To that end, a device known as a double pendulum has been constructed and it's end point tracked through the use of a small LED light.
Normally, a pendulum has the characteristic of being a strongly deterministic and mathematically easy to understand device. It's path easily predictable/computable even when examined in non-idealized conditions that include friction and air resistence.
A double pendulum, which is essentially a pedulum attached to a pendulum, although equally mathematically predictable assuming ideal conditions, exchibits extraordinerily complex behavior in real world conditions, their patterns deviating strongly from the mathematically predicted one. As the pendulum(s) constantly reach equilibrium points and exchange momentum and energy, small differences in the ambient conditions or the construction of the device can send the second pendulum in a completely different path and direction than expected. The movement of the second pendulum becomes chaotic, and in fact is so sensitive to the initial/local condition that even when released from the exact same point it will commit to a different path every time.
As a further step, I tried to extrude the paths from a couple of the photographs and superimpose them on top of each other, that way essentially quickly creating a "statistical" diagram showcasing where the pendulum had the greater chance to be during that photographic series sample.
Predictably the diagrams are heavy at the bottom since ultimatly gravity brought both pendulums at a stop, with the last few swings following the least energy intensive arcs that approach the lowest energy point. However a surprise was that the device seemed to have a bias towards the right side, thus revealing a further pattern within the patterns. (a simple strange attractor). The exact causes of that are unknown, but has to do with the imperfections of the device, like it not being perfectly straight / imbalances in the construction / friction changes in the joints of the pendulums / vibrations of the main support itself etc...
It is a pattern that someone can only see in the analog world, unique to this particular construction and a reminder of how chaotic influences can cause real world objects to deviate from their idealized mathematical models.
Predictably the diagrams are heavy at the bottom since ultimatly gravity brought both pendulums at a stop, with the last few swings following the least energy intensive arcs that approach the lowest energy point. However a surprise was that the device seemed to have a bias towards the right side, thus revealing a further pattern within the patterns. (a simple strange attractor). The exact causes of that are unknown, but has to do with the imperfections of the device, like it not being perfectly straight / imbalances in the construction / friction changes in the joints of the pendulums / vibrations of the main support itself etc...
It is a pattern that someone can only see in the analog world, unique to this particular construction and a reminder of how chaotic influences can cause real world objects to deviate from their idealized mathematical models.
