a place to cold some processing sketches I made while in the office
ravenWordsp uses the ttslib https://www.local-guru.net/blog/pages/ttslib
ravenWordsp does not work in processing 4, because of the library, but i will work with processing 3
“On a wall surface, any continuous stretch of wall, using a hard pencil, place fifty points at random. The points should be evenly distributed over the area of the wall. All of the points should be connected by straight lines. “ -Wall drawing 118
A complete graph also called a Full Graph it is a graph that has n vertices where the degree of each vertex is n-1. In other words, each vertex is connected with every other vertex.
https://mathworld.wolfram.com/CompleteGraph.html
Now, you have n vertices in total, so you might be tempted to say that there are n(n−1) edges in total, n−1 for every vertex in your graph. But this method counts every edge twice, because every edge going out from one vertex is an edge going into another vertex. Hence, you have to divide your result by 2. This leaves you with n(n−1)/2.
is a modular mult. line art with simple polar coordinates. You can click around to get differnt multiples and points on the circle if theta gets high it starts to get out of phase and drift see some images at my instagram
the waves are drawn with no loops, one loop and two loops and either scroll or not
https://www.instagram.com/p/CY4IIRYoNmR/
https://www.instagram.com/p/CY6aNSPIo05/
Sandpile with numbers of grains of sand in each cell. There is a 2d array that keeps track of the number of grains at the cells x y position. The max number of grains of sand in a cell is 3. The ‘#’ indicates that the cell contains 4 or greater. If a cell has four or greater it gives up one grain to each of its 4 neighbors (NSEW neighbors not all eight neighbors). The next generation of the board is done like the game of life. A second array keeps track of the changes, so not to overwrite changes on the original. When all the cells are checked and all the overflows for one generation are updated the original array is set to the new array and the process repeats. There is a great #numberphile video, #thecodingtrain code challenge and most recently Jordan Ellenberg’s https://nautil.us/issue/107/the-edge/the-math-of-the-amazing-sandpile #creativecoding #processing #math #sandpile #p5js #math
have done some more work on the sand piles not with simpler with one loop.
have also made a version on a torus using modulo
the large amout dropped in the center will then continue forever with some interesting patterns
doubling time is seen. I havent found a good setting for a chaotic mess but I am sure it is there
I have also made a version to place many grains of sand in all of the cells
bu this looks better when it is on a closed plane not a tours
I have uploaded all of these versons. I have not improved the earlier versions with one loop
but I will make a seperate repo for sand piles and make a p5 version to use on the web
here is a Sierpiński carpet made with points from a simple chaos game. I originally coded this on my phone in the office. I had forgotten about it and was reminded when I saw this great video by Mr. Sparks The Chaos Game - Geogebra Build - as seen on Numberphile
He is using geogebra but his explanation of the Hausdorff dimension is great in the third part of the video
the carpet is:
- 3 times bigger in length
- 8 copies
- so 3 to what power is 8
- 3**x = 8
- fd = log(8)/log(3)
- The Hausdorff dimension is log(8)/log(3) == 1.892
https://www.instagram.com/p/CZcKHE8oJKi/
Pulling a two dimensional square into the third dimension as Sierpinski Tetrahedron, using the chaos game in processing P3D. 3D is fast, each frame I am plotting over 10,000 points half way to one of four original points. if it is only plotted in 2d this would create a solid square. but by putting one point into the third dimension it produces an object that has a Hausdorff dimension of 2 in 3d space. using PVector and built in lerp function. #math #creativecode #processing #p5js #chaos #fractal
https://www.instagram.com/p/CZejeDkoLN2/
Some more 3d chaos game. This time the Menger sponge. The 20 points are put into an array as vectors. One of the points is randomly picked. Then the plotting vector is calculated as 2/3 the way to that point using the PVector lerp() function. The color is mapped to the index of the points in HSB mode. creates a complex image with just a little bit of code. #math #creativecode #processing #p5js #chaos #fractal #creativecoding
so what is the Hausdorff dimension of the Menger sponge. Let's look at how it is created by scaling. The length scales by 3.
regular cube
- so let's look first at scaling a regular cube by three
- if we scale by three there will be 27 copies
- so we can get the dimension d by (scale factor: 3) raised to what (power d) = (copies: 27)
- 3^d = 27
- d= 3 : 3^3 = 27
- the dimension is 3. It is 3 dimensional.
Menger Sponge
- The Menger Sponge is also scaled by 3
- but the Menger Sponge has only 20 copies (in the code they are the original 20 vectors, the other 7 are its distinctive holes)
- so dimension is d is (scale factor:3) raised to what (power d) = (copies: 20)
- 3^d =20
- we know d is less than 3, and greater than 2, 3^3=27, 3^2 = 9
- we can get the dimension using logs
- log(3^d) = log(20)
- d*log(3) = log(20) (we can move the exponent out using the power rule of logs )
- d = log(20)/log(3)
- d = 2.72683
- this is a fractional dimensions (where the name fractal originates)
https://www.instagram.com/p/CZrmjMQo2ov/
Reading "The Recursive Universe" from 1985 by William Poundstone and making a variation of Ulam's coral reefs as described in chapter 8. This Ulam type CA applies just a single rule while checking the north, south, east, and west neighbors, also called the von Neumann neighborhood. But it also takes into account the generation the cell was born. If the sum of the neighbors divided by the generation = 1 then then that cell is comes alive or redrawn with a color matching its generation. So even older parts of growing coral get recolored or filled in with different colors creating nice variation.
The book is a great exploration of cellular automata and how these models can help explain life and the universe.
added a version on a torus: it it is more symmetrical over 1000 generations
Euler spirals inspired by NumberPhile https://youtu.be/kMBj2fp52tA the turtles name is greg he is a pvector that is updated in a forward function using polar coordinates and a right turn function he has a heading angle intheta he can be sent a plot theta in the right(); angles are in degrees converted to radians in the forward() and right() functions
a very simple function to create n polygon using polar to cartesian coordinates
just remember that you must convet and int to a float if you are doing division
void drawpoly(int n) {
for (int i =0; i<n; i++) { // 1/n gets a number less than zero that when multipled by TWO_PI gets the angel in radians
float angle = i/float(n) - 0.25; //need to convert to a float
//println(angle);// the - 0.25 makes the image straight
float vx = radius * cos(angle *TWO_PI);
float vy = radius * sin(angle*TWO_PI);
float v1x= radius * cos((angle+1/float(n))*TWO_PI);
float v1y= radius * sin((angle+1/float(n))*TWO_PI);
line(vx, vy, v1x, v1y);
}
}the same simple function with lerp lines from the center