..again: lot's of interesting mail today... 
21022006 From The Nonlinear Workbook by WilliHans Steeb ( ISBN 9812562788 ) : Onedimensional maps 1.1 Exact and Numerical Trajectories
[Warning: the 'music' you are about to hear is rather irritating  mind your neighbours]
MINENONEMANEMU This flash animation moves to one of twelve frames dependent on the value of X%12
until the period orbit ...421421... is reached. While moving towards its period orbit it also stores the values in an array.


<UNFOLD>
The function in grey above is a simple linear function, utterly predictable. Given a certain input, a real number, it will create a map of real numbers leading to its period orbit ...421421... by taking its output as new input for the same equation. This happens in fully predicatable manner. Nothing weird or nonlinear about it.
So there's no answers here and hardly any art, but i took it as a starting point for yet another string of things inside the Cathedral. Somehow i feel i have to learn about things like the RuelleTakensNewhouse Scenario, Hopf Bifurcations and Heigway's Dragon, so if you're interested too, i'd be glad to take you along my dummie trail. Like most of you, i know next to nothing on these subjects, but I do know a tiny bit of coding so i 'll be very explicit about how to translate all the Mathematical Beauties to 'real world' java examples. Sure, this takes place within the Cathedral, so you may expect some irregularities along the path, and as you should know by now, nothing here gets completed or substantial without it proving it's worth to Our Lady CathedralMother Dear. In other words, as usual, i start these things on stupid impulse, & no one can tell what may come of it. Now i know there do exist some good introductions out there, but i can't bring myself to going through all that, just reading it. I need to be doing something with it, otherwise i just clean forget everything i read. That, i think, about covers the Why of things. 

There's a boring start to all subjects, so here's the 'Hello World' of (Non)linearity: the onedimensional maps below take the instant of their creation as an input (request time of this file + the time it takes to compute the previous maps), effectively showing their computation takes time. Wow, spec  ta  cu  lar! Well, at least it clearly shows that linearity in functions doesn't lead to predictable outcomes when applied in the real world. Time is a nasty bugger and we need to keep a clear picture of things as they happen. Math is math, code is code, running code is running code and people discussing the real world all need to be addressed on their own plane of consistency. As you can see, a lot of things can happen between those spaces in a split second. Finally, visualisations like these may not give you a better understanding of the mathematics that underlie them, and math itself doesn't need it much or not at all, but they may be a welcome alternative to the tempting images of mystification that come to (my) mind (at least) when i think of the names mentioned above or hear someone mentioning them in real world language that he or she claims matters to me as well. If i don't understand, at least i can see what i don't understand. So perhaps this coding business is about a very private form of ownership or lack thereoff, after all. </UNFOLD> © dv 2006  Free Art License  L.M. December 31, 2016 11:32 PM 

<%@ page contentType="text/html;charset=utf8" language="java"
import="java.math.*"%> 

<% // first use a boolean to alternate tables boolean mod=true; StringBuffer sb=new StringBuffer(); for (int k=6;k>0;k){
%> 

//in one html table give results for f(x) with original input the time of the users request in Milliseconds sinds january 1 1970 descending to when the function reaches the period orbit ...421421... Date d=new Date(); String tijd=""+d.getTime(); BigInteger X= new BigInteger(tijd); BigInteger TWO= new BigInteger("2"); BigInteger THREE= new BigInteger("3"); int T=350; for (int t=0;t<T;t++){
} 
<% //in another table give the same results ascending for (int i=349;i>0;i){
} %> 

<% }else{ mod=true; %> 

<% //turn around the sequence of tables first use what's still in the StringBuffer for descending output at the end of this table be sure to empty the StringBuffer thus sb.delete(0,sb.length()); //insert the artcode stuff anywhere between the tables //because the computation takes quite some time, you get different dates to refer to (ususally one second will elaps, if not, someone upgraded my server). Do not do this (a lot) on your site, the application server does not like all that work. //if you refresh the page a few times, you'll see that for some amount of milliseconds (the input), the function reaches its period orbid, for others it doesn't. It would, eventually if you change the iteration from 350 to sth higher, say 700. //in the next episode we'll start using Processing to avoid all of this Server Stress. Surprisingly, the user's computer can count too, so we don't need Big Mama. & JSP spaghetti is nice because it looks more complicated, but it's also unnecessarily confusing... }//you opened a for loop up there, remember? 

CODEART is not a question 
Relevant Math articles in Wikipedia 
<%
Date d=new Date();
String tijd=""+d.getTime();
BigInteger X= new BigInteger(tijd);
BigInteger TWO= new BigInteger("2");
BigInteger THREE= new BigInteger("3");
int T=350;
for (int t=0;t
<%for (int i=349;i>0;i){
out.print(sb.toString().split("::")[i]+" "); }%> 
<%for (int i=349;i>0;i){
out.print(sb.toString().split("::")[i]+"
<%
Date d=new Date();
String tijd=""+d.getTime();
out.print(" "+d+" & code is more important than art 
<%} }%>
If you have the time, please place comments on the no comments place please 

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