Hey, Do You Got Juvenoia?  Heres A Video For You: https://www.youtube.com/watch?v=LD0x7ho_IYc :)

Hey BAB, could you please share the code to this? Im on the way to learn some processing and this is the kind of code i would like to learn. So, please share, so i can learn from it :)

Take care mate!

rgb knot

Here’s the orginal creator, he’s a legend:

beesandbombs (http://beesandbombs.tumblr.com/)

Take care

Waving Circles 

Remake of this awesome gif (does anyone know the original creator?): https://33.media.tumblr.com/a5d2523e8a4fc92e1629ae9937d870f6/tumblr_nl4lm8O73g1u93xcqo1_500.gif

This is early days for my conversion to p5.js. Here’s the code: http://jsfiddle.net/dandersod/8uL4s35d/

Welcome to my world of dyslexia... :)

When I'm halfway through a sentence and suddenly realise there is no way out of the grammatical crater I have dug myself

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.

Wow! You have come real far with this now! Amazing work. Keep it up!

Mechanics of Form. Work in progress.

Back when I was in school, this concept was really hard for me to grasp my head around, and I must say, this was a compelling way to understand the function of multiplying with negative numbers!

Thanks!

By virtue of everyday usage, the fact that (-1) x (-1) = 1 has been engraved onto our heads. But, only recently did I actually sit down to explore why, in general negative times negative yields a positive number !

Intuition.

Let’s play a game called “continue the pattern”. You would be surprised, how intuitive the results are:

2 x 3 = 6

2 x 2 = 4

2 x 1 = 2

2 x 0 = 0

2 x (-1) = ??  (Answer : -2 )

2 x (-2 ) = ?? (Answer : -4 )

2 x ( -3) = ?? (Answer : -6 )

The number on the right-hand side keeps decreasing by 2 !

Therefore positive x negative = negative. 

2 x -3 = -6

1 x -3 = -3

0 x -3 = 0

-1 x -3 = ?? (Answer : 3)

-2 x -3 = ?? (Answer : 6)

The number on the right-hand side keeps increasing by 3.

Therefore negative x negative = positive.

Pretty Awesome, right? But, let’s up the ante and compliment our intuition.

The Number Line Approach.

Imagine a number line on which you walk. Multiplying x*y is taking x steps, each of size y.

Negative steps require you to face the negative end of the line before you start walking and negative step sizes are backward (i.e., heel first) steps.

So, -x*-y means to stand on zero, face in the negative direction, and then take x backward steps, each of size y.

Ergo, -1 x -1 means to stand on 0, face in the negative direction, and then take 1 backward step. This lands us smack right on +1 !

The Complex Numbers Approach.

The “i” in a complex number is an Instruction! An instruction to turn 90 degrees in the counterclockwise direction. Then i * i would be an instruction to turn 180 degrees. ( i x i = -1 ). where i = √-1

Similarly ( -1 ) x i x i = (- 1 ) x ( -1 )= 1. A complete revolution renders you back to +1.

We can snug in conveniently with the knowledge of complex numbers. But, complex numbers were established only in the 16th century and the fact that negative time negative yields a positive number was well established before that.

Concluding remarks.

Hope you enjoyed the post and Pardon me if you found this to be rudimentary for your taste. This post was inspired by Joseph H. Silverman’s Book - A friendly Introduction to Number Theory. If you are passionate about numbers or math, in general it is a must read.

There are several other arithmetic methods that prove the same, if you are interested feel free to explore.

Have a Good Day!

PC: mathisfun

More of the noise. Lovely to look at!

Flow fields, click for higher resolution.

Verkligen en vacker skapelse!

Golden rectangle

Master of geogebra helped me out with this! Thanks!

Table Saw

@mrvmt requested a table saw sketch, and this is the first draft. In GeoGebra here.

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