Wow, This Is The Coolest Comic I Ever Read! Got Your Book (”What If?”) And Now Think Its The Second

Beautiful, where can I get my hands on one of these? :) 

Dragon Fractal - Level 5

If you take each of the 4 sides of a square and modify the angle of the dragon fractal as you go up, you get this shape. I’m still fighting the 3d models to get a nice smooth version.

Numberphile (https://www.youtube.com/channel/UCoxcjq-8xIDTYp3uz647V5A) Got some good videos on the subject.

Heres one that introduce the topic: https://www.youtube.com/watch?v=aqyyhhnGraw

Did you know that there’s a whole branch of topology called knot theory studying knots?

Find out more here: https://en.m.wikipedia.org/wiki/Knot_theory

Infinite Trees Are Super Weird

Trying to list all the numbers, yet again... The Infinite Series playlist: https://www.youtube.com/playlist?list=PLaNzoFtkQ7rYwjp8AlVBp576YK_sdfyi8

Finally Vihart post a video again!

Geometry apps!

I have stumble upon some of the neatest apps, for a person like me that love geometry, these apps are just what I’ve been looking for!

Euclidea:

IOS: https://itunes.apple.com/app/id927914361 Android: https://play.google.com/store/apps/details?id=com.hil_hk.euclidea This app is only Euclidean geometry, that’s what I like the most. Appinfo: Euclidea is a brilliantly original way to learn about, explore and have fun with Euclidian Constructions! Your task is to solve interesting challenges by building geometric constructions with a straightedge and compass. If you design the most elegantly simple solutions in the least number of moves, you’ll earn the highest scores. Solutions are scored in lines (L) and elementary Euclidean constructions (E).

XSection:

IOS: https://itunes.apple.com/us/app/xsection/id1069933287?mt=8 Haven’t found it on Android yet, but this app aims to learn you about Polyhedrons, cross sections and geometry. Appinfo: Learn how to construct cross sections of polyhedrons. Study different techniques, train yourself, and then solve geometric puzzles. 

Pythagorea:

IOS: https://itunes.apple.com/us/app/pythagorea-geometry-on-square/id994864779?mt=8 Android: https://play.google.com/store/apps/details?id=com.hil_hk.pythagorea&hl=sv Just found this game, so I paste the appinfo: Pythagorea is a collection of geometric puzzles of different kind that can be solved without complex constructions or calculations. All objects are drawn on a grid whose cells are squares. A lot of levels can be solved using just your geometric intuition or by finding natural laws, regularity, and symmetry. 

Pythagorea60:

IOS: https://itunes.apple.com/us/app/pythagorea-60-geometry-on/id1043064990?mt=8 Android: https://play.google.com/store/apps/details?id=com.hil_hk.pythagorea60&hl=sv Just found this game, so I paste the appinfo: Pythagorea 60° is a collection of more than 270 geometric problems of different kind that can be solved without complex constructions or calculations. All objects are drawn on a grid whose cells are equilateral triangles. A lot of levels can be solved using just your geometric intuition or by finding natural laws, regularity, and symmetry. 

Horis International Limited

All these games are made from the same developer, Horis International Limited:  IOS: https://itunes.apple.com/us/developer/horis-international-limited/id646324304 Android: https://play.google.com/store/apps/developer?id=HORIS+INTERNATIONAL+LIMITED Big up, love this!

Would like a map of the whole area, just to know for sure i’ve been to all the places :)

Wow, this is the coolest comic i ever read! Got your book (”What if?”) and now think its the second coolest thing i read! :) Keep it up!

Damn, yes, why wouldn’t you! Looks great!

idk, why wouldn’t I make these and post them

Does this post explain this aswell? https://www.youtube.com/watch?v=uENITui5_jU

The Strobe Light Conundrum

The post - Illusion of Perception obviously confused a lot of people since I have been getting a lot of requests to explain it again.

Let me try it again with another animation.

The setup

The illusion of falling droplets is created by a pump which is pushing out the water droplets at a fixed rate. ( call it X ) - Does NOT change.

Changing the frequency of the strobe light ( call it Y ) is the integral part of the illusion.

The flow is similar to that of your shower head. The water droplets are continuously falling down. With the strobe light, we are just illuminating the droplets at different instances of time.

When  X = Y  —>  The droplets appear stationary.

Imagine yourself to be sitting on top of the hose and watching every drop fall through. Whenever the droplet of water is about to leave the hose, the light flashes. This renders the droplet as stationary.

Let us call the distance between the droplets as L.

When Y > X  — > The droplets appear to move up.

Now, the strobe light flashes a little too quickly than the rate of the drop falling. This gives us the illusion of droplets moving up since you are flashing the light before the droplet has traversed the distance L.

When Y < X  — > The droplets appear to move down.

Now, the strobe light flashes a little slower than the rate of the drop falling. This gives us the illusion of droplets moving down since you are flashing the light after the droplet has traversed the distance L.

Thank you so much for expressing your concerns and I apologize if it had confused you. I hope this post made it up

Have a good day :)

EDIT - Here is the actual gif from the illusion of perception post.

"Oh captain, my captain."

Regolo’s Square Fractal

Inspiration: http://regolo54.tumblr.com/post/150627614707/fractal

Code as is.

Interactive code. Up/down/left/right mouse controls the size and placement of the squares. Up/Down arrows control how many squares are in each ring. Any other key will save the frame as a picture!

How beautiful! 

Fibonacci you crazy bastard….

As seen in the solar system (by no ridiculous coincidence), Earth orbits the Sun 8 times in the same period that Venus orbits the Sun 13 times! Drawing a line between Earth & Venus every week results in a spectacular FIVE side symmetry!!

Lets bring up those Fibonacci numbers again: 1, 1, 2, 3, 5, 8, 13, 21, 34..

So if we imagine planets with Fibonacci orbits, do they create Fibonacci symmetries?!

You bet!! Depicted here is a:

2 sided symmetry (5 orbits x 3 orbits)

3 sided symmetry (8 orbits x 5 orbits)

5 sided symmetry (13 orbits x 8 orbits) - like Earth & Venus

8 sided symmetry (21 orbits x 13 orbits)

I wonder if relationships like this exist somewhere in the universe….

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