How and why to take a logarithm of an image [video]

I've been loking into how 3B1B builds their rendering pipeline, and it's honestly mind blowing. They use Python along with custom OpenGl shaders to handle most of geometric transformations, shich seems to be what creates those "brain breaking" visual effects.It's fascinating how our visual cortex tries to interpret overlapping geometric patterns and ends up producing such counterintuitive perceptions. Shat I still can't quite wrap my hand around is... to what extent are these effects caused by the rendering itself, and how much of it is just how our brain interprets the visual information?

Similarly, it's possible to take the derivative of a song. You can use a Fourier transform to express the song's waveform as a series of sin and cosine functions, then take the derivative.

Imagine, for the sake of simplicity, you could express the song's waveform with the function 13 * sin(41x).

The derivative of this function is 533 * cos(41x).

Cosine, of course, is just a phase shifted sine, and the constant coefficient inside the function stays the same. So you're not changing anything about the shape of the wave, just stretching it vertically.

This has the effect of mimicking a "high pass filter," amplifying the volume of the highs.

This video is an absolute tour de force of communicating a complex concept.

The title I get when I click on this is, "How (and why) to take a logarithm of an image"

This kind of technique can be used in 3D space as well! The analysis here represents Escher's techniques as conformal maps in the complex plane. Conformal maps are also possible, though more limited, in R^3. This is something that I explored some years ago and wrote an article about it, though it focuses more on graphics than math: https://www.osar.fr/notes/logspherical/

I've been wondering if you could do a similar thing for a Droste effect image containing two copies of itself. Packs of Laughing Cow cheese show a cow with two earrings, each of which is a pack of the cheese.

Those videos are awesome! 3B1Bs visualizations finally made e^(pi*i) make sense.

His videos on Euler's formula inspired me to make a silly toy so I could play with it myself.

https://gitlab.com/aprentic/complex-viz/

I love 3B1B but generally don't have time to watch long videos. Can anyone sum up the punchline?

Makes me wonder how this would look/feel interactively if a game world was rendered like this

Clickbait title broke my brain.

Clickbait title could use another pass. What is this about?