Magnitude of a 3D vector

Here Simon explains how to calculate the magnitude of a 3D vector. This is something he partially figured out on his own and partially learned from Daniel Shiffman’s tutorial on Trigonometry and Polar Coordinates.

 

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Infinite Line in Processing. Simon’s own code.

A beautiful project in Processing (Java), Simon’s own code, resembling  an El Lissitzky painting that you can control and change with the mouse (without Simon knowing El Lissitzky). Resulted from thinking about and playing with infinite line and line segments. Simon used the following formula: slope times x plus yIntercept.

Infinite Speceship 13 Jun 2017 2

Infinite Speceship 13 Jun 2017 1

 

 

 

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Pendulum Force

This is a beautiful “lecture” that Simon in his pajamas, chocolate paste adorning is face, game me Friday morning. He spoke about pendulum force, a force he was about to apply in a coding project.

The other videos form the very beginning of the lecture, with Simon plays with sine and cosine and explains why location, velocity and acceleration can be vectors and can be angles:

And this is the code where pendulum force is used. It’s an example from The Nature of Code book by Daniel Shiffman, from Chapter 3 on Oscillation:

Oscillation and Drag Force: Spring Project.

Today Simon was watching Daniel Shiffman’s tutorials to learn about drag force and how to apply it when building a spring simulation in p5.js. Simon wrote the formula for drag force in Microfost Word and looked up all the variables:

Drag Force 23 Apr 2017 2

While building a spring in p5.js, Simon talks about the 3 laws of Isaac Newton:

The project is based upon Daniel Shiffman’s book The Nature of Code, specifically Chapter 3 (Oscillation). Simon spent the rest of the evening studying “simple harmonic motion”, periods and amplitudes. Here is an excerpt from Daniel Shiffman’s book:

y = sine(x)
You’ll notice that the output of the sine function is a smooth curve alternating between –1 and 1. This type of a behavior is known as oscillation, a periodic movement between two points. Plucking a guitar string, swinging a pendulum, bouncing on a pogo stick—these are all examples of oscillating motion.
This is what is known as simple harmonic motion (or, to be fancier, “the periodic sinusoidal oscillation of an object”). It’s going to be a simple program to write, but before we get into the code, let’s familiarize ourselves with some of the terminology of oscillation (and waves).
Simple harmonic motion can be expressed as any location (in our case, the x location) as a function of time, with the following two elements:
  • Amplitude: The distance from the center of motion to either extreme
  • Period: The amount of time it takes for one complete cycle of motion
Looking at the graph of sine, we can see that the amplitude is 1 and the period is TWO_PI; the output of sine never rises above 1 or below -1; and every TWO_PI radians (or 360 degrees) the wave pattern repeats.

L-Systems

What sort of literature do you fancy in the evening? Simon’s downloaded the book The Algorithmic Beauty of Plants tonight.

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Here Simon explained to me how L-systems and Cantor Set worked:

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An L-system or Lindenmayer system is a parallel rewriting system and a type of formal grammar. An L-system consists of an alphabet of symbols that can be used to make strings, a collection of production rules that expand each symbol into some larger string of symbols, an initial “axiom” string from which to begin construction, and a mechanism for translating the generated strings into geometric structures.

Simon says that an L-sestem is “also a context-free grammar that can have infinite generations”.

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The Cantor set is a set of points lying on a single line segment that has a number of remarkable and deep properties.

Simon followed the book and Daniel Shiffman’s tutorial on L-Systems to create beautiful trees and other recursive patterns in

http://turtleacademy.com/playground/en

and

http://www.kevs3d.co.uk/dev/lsystems/#

L_System Fractal Trees 15 Apr 2017 1

L_System Fractal Trees 15 Apr 2017 2 square brackets around last F

L_System Fractal Trees 15 Apr 2017 2

L_System Fractal Trees 15 Apr 2017 23

L_System Fractal Trees 15 Apr 2017 4

And “what you also might need by an L-system is a String Buffer”:

String Buffer (might need by L system) 15 Apr 2017 2

Triangle Numbers. Simon’s own code

Now this was pretty amazing! Simon’s new own code, that he so nonchalantly wrote while “having a break” from practicing recursive functions, generates “triangular numbers”.

A triangular number or triangle number counts the objects that can form an equilateral triangle. The nth triangular number is equal to the sum of the n natural numbers from 1 to n. The sequence of triangular numbers is

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406 …

https://www.youtube.com/watch?v=Y2QaShP8vHY

 

“This particular piece of code works with any sequence”, Simon said:

Triangle Numbers (This particular piece of code works with any sequence) 15 Apr 2017

He tried to build the whole triangle but got stuck.

Recursive Function: Sierpinski triangle

Simon followed Daniel Shiffman’s Fractal Recursion tutorial on how to write functions in Processing that call themselves (recursion) for the purpose of drawing fractals.

Later he programmed a Sierpinski triangle from memory, using circles. A Sierpinski triangle is a fractal set with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles. Originally constructed as a curve, this is one of the basic examples of self-similar sets, i.e., it is a mathematically generated pattern that can be reproducible at any magnification or reduction. It is named after the Polish mathematician Wacław Sierpiński, but is actually a reincarnation of Pascal’s triangle.

 

 

 

Connections Project in Java (Simon’s own code)

Simon built another project of his own design. His program allows to draw intricate patterns that resemble Islamic tiling, the building block being a polygon of your choice.

First, you can enter the number of vertices that you wish your polygon to have and the program does the rest: connecting all the vertices inside the polygon. This part of code is also available in JavaScript. Play with Simon’s code here:  https://alpha.editor.p5js.org/simontiger/sketches/Hyr8m59ax

Simon explaining how it works:

Multiple polygons:

Simon later corrected the bug in his code (removed the empty space in between the polygon tiles):

Connections 11 Apr 2017