Comments on: Bicycling for Collatz

By: lifeh2o

lifeh2o — Thu, 25 Mar 2010 11:47:45 +0000

Hey!! thats great work, i was thinking almost the same thing from some days, i made a script in Processing where all numbers are written in a line.
A curve is drawn over all multiples of a number
For example if there will be small curve on 2 to 4, 4 to 6, 6 to 8 ……
a bigger curve will be there on 3 to 6, 6 to 9 , 9 to 12 …..

import processing.dxf.*;

import netscape.javascript.*;

import ddf.minim.signals.*;
import ddf.minim.*;
import ddf.minim.analysis.*;
import ddf.minim.effects.*;

import processing.net.*;
import processing.opengl.*;

void setup(){
PFont font;
font = loadFont(“ArialMT-18.vlw”);
textFont(font);
size(300,800);
Numbers n;
n = new Numbers();
//n.createnumbers();
n.createarcs(2,100,radians(-90), radians(90));
n.createarcs(3,100,radians(90), radians(-90));
n.createarcs(4,100,radians(-90), radians(90));
n.createarcs(5,100,radians(90), radians(-90));
n.createarcs(6,100,radians(-90), radians(90));
n.createarcs(7,100,radians(90), radians(-90));
n.createarcs(8,100,radians(-90), radians(90));
n.createarcs(9,100,radians(90), radians(-90));
n.createarcs(10,100,radians(-90), radians(90));
n.createarcs(11,100,radians(90), radians(-90));
n.createarcs(12,100,radians(-90), radians(90));
n.createarcs(13,100,radians(90), radians(-90));
}

class Numbers {
int alignx=120;
int aligny=14;

Numbers(){

}
void createnumbers(){
for (int i=1; i<=1000; i++){
fill(100);
text(i,alignx,i*aligny);
}
}
void createarcs(int val, int limit,float astart, float aend){
for (int i=0; i<=limit; i++){
noFill();
//arc(x, y, width, height, start, stop)
arc(alignx, i*aligny*val+(aligny/2)*(3*val-1), aligny*val, aligny*val, astart, aend);
}
}
}

/*
val
1-14=(14/2)*(3*val-1)+14*val*i — 28,42,56
2-35=(14/2)*(3*val-1)+14*val*i — 63,91,119
3-56=(14/2)*(3*val-1)+14*val*i — 98,140,182
4-77=(14/2)*(3*val-1)+14*val*i —

aligny/2 * (3x+2ix-1)
*/

The idea behind this was that, for each number before which there is no multiple of it is a prime, so in the graph the number from where the curve starts is a prime.
I hope graphviz would help me doing more experiments

By: lifeh2o

lifeh2o — Thu, 25 Mar 2010 11:47:03 +0000

import processing.dxf.*;

import netscape.javascript.*;

import ddf.minim.signals.*;
import ddf.minim.*;
import ddf.minim.analysis.*;
import ddf.minim.effects.*;

import processing.net.*;
import processing.opengl.*;

class Numbers {
int alignx=120;
int aligny=14;

Numbers(){

/*
val
1-14=(14/2)*(3*val-1)+14*val*i — 28,42,56
2-35=(14/2)*(3*val-1)+14*val*i — 63,91,119
3-56=(14/2)*(3*val-1)+14*val*i — 98,140,182
4-77=(14/2)*(3*val-1)+14*val*i —

aligny/2 * (3x+2ix-1)
*/

The idea behind this was that, for each number before which there is no multiple of it is a prime, so in the graph the number from where the curve starts is a prime.

I hope graph viz would help me doing more experiments

By: Tiempo finito y logarítmico » Grafos de Collatz

Tiempo finito y logarítmico » Grafos de Collatz — Mon, 10 Mar 2008 05:15:42 +0000

[...] intentando hacer exactamente esto; afortunadamente en Bicycling for Collatz hay gráficas ya hechas e instrucciones para generarlas con Haskell y Graphviz. El gráfico [...]

By: Bryan O'Sullivan

Bryan O'Sullivan — Fri, 23 Feb 2007 22:16:44 +0000

Very pretty.

By: Code//Design » Amazing Graphviz Plots

Code//Design » Amazing Graphviz Plots — Fri, 23 Feb 2007 01:07:51 +0000

[...] Ok, check out these graphviz plots! [...]