A list of puns related to "Iterated Function System"
I recently wrote a terminal app for rendering fractals from iterated functions systems using linear contraction mappings on either R^1 or R^2.
I've been using it to quickly get an idea of what type of attractor to expect when working with IFS's and to render silly/pretty gifs.
Thoughts and opinions are very welcome!
thanks :)
Let's say I have an expression: x . x . x . x ... of arbitrary length, where each (.) is some non-associative, non commutative operation on the value x, and x . (x . (x . x)) is the default order of operations. Is there a concise way of representing and ordering all the different ways we can change the order of operations here with parentheses?
Note I only use length four here for example purposes. I'm need a system to come up with and notate shortly all the unique ways of doing this. Thanks!
Edit: Added the non commutative/associative detail; should have included it first draft.
I recently wrote a program for a class that draws a Sierpinski triangle using an iterated function system. They gave me algorithm to use and I successfully created a program with it. The problem is I do not understand why it works. I was hoping math may be able to help me out.
Algorithm:
The new points are iteratively computed by randomly applying (with equal probability) one of the following three coordinate transformations:
xn+1 = 0.5 xn yn+1 = 0.5 yn;
xn+1 = 0.5 xn + 0.25 yn+1 = 0.5 yn + 0.5 (sqrt(3)/2);
xn+1 = 0.5 xn + 0.5 yn+1 = 0.5 yn;
I googled a bit and could not find an explanation that made sense to me.
Edit: Found that each equation fills in a certian part of the triangle. Color coded by equation: http://i.imgur.com/dLmvOva.png
Please help.
I've been teaching myself about the Heighway Dragon Curve
I read the Wikipedia page for both the Dragon Curve and the Iterated Function System, but I still couldn't make heads or tails of it. I tried looking at the IFS for other fractals (IE:sierpinski) as an example that I could extrapolate from, but I could not understand those either.
My questions refer directly to the Heighway Dragon Curve IFS:
What does s0 represent? Is that a single point with coordinates (x,y)=(0,1)?
What does variable z represent?
I assume i represents iterations, right?
What does f1 and f2 output exactly?
If I could see an example, or have someone walk me through step by step how the IFS equations generate the Dragon Curve, I would greatly appreciate it.
http://en.wikipedia.org/wiki/Dragon_curve#Heighway_dragon
I'm a beginner when it comes to this topic. But I was always fascinated by one observation. Let's consider a function [;f: A\subset \mathbb{R} \to \mathbb{R};]. Now let us consider a sequence [; f^(n=) \begin{cases} \mathrm{id_A}, & n=0\ f\left(f{n-1} \right) & n>0. \end{cases} ;] If this sequence has a fixed point [;x_0;] and [;f<\mathrm{id_B};] for some [;B\subset A;], is it true that the sequence is convergent on [;B;] to [;g\equiv x_0;]? How about multiple fixed points? Do you have any books on the topic thant won't kill me with their jargon?
< Update> I replaced recursion using stack. Thanks for your help, I learned a lot. Here is the stackexchange answer that helped me: https://codereview.stackexchange.com/questions/163601/iterating-an-array-of-nodes-each-of-which-can-have-children . The snippet used in the answer:
static void IterateNodes(Node[] nodes)
{
foreach (var node in nodes)
{
var stack = new Stack<Node>();
stack.Push(node);
while (stack.Count > 0)
{
Node current = stack.Pop();
Console.WriteLine(current);
var childrenRightToLeft = current.Children.AsEnumerable().Reverse();
foreach (var child in childrenRightToLeft)
{
stack.Push(child);
}
}
}
}
</update>
I want to set a specific property of an object and also of its children. The first (and only) solution that came to my mind is a recursive one:
void _lui_object_set_need_refresh(lui_obj_t *obj)
{
obj->needs_refresh = 1;
for (uint8_t i = 0; i < obj->children_count; i++)
{
_lui_object_set_need_refresh(obj->children[i]);
}
}
The above function set need_refresh
property of the object and of its children recursively. But, must I convert it to an iterative function? If yes,
Just something I noticed and thought people here might find it curious too:
Suppose you have some constant, let's call it M
, and a function f(n)
that maps the set of digits in base b to itself.
Let's also define F(x)
as the result of replacing each digit of x
with output of f(n)
for that digit.
Given an initial value A, we can construct a sequence:
x_0 = A
x_n = F(M * x_(n-1))
Despite this family of sequences being seemingly simple, in general there's no algorithm to determine if such a sequence will grow indefinitely or if at some point it'll reach a cycle or converge to some value.
It's not very complicated to see why this would be the case, as we can easily find f(n)
and M
that would simulate another undecidable system, for example a Turing-complete cellular automaton (rule 110).
Let's say we're working in base 10, M
is set to be 42.1 and f(n)
turns digits 6, 5, 3, 2 and 1 into 1 and other digits into 0. If we multiply a number consisting only of decimal digits 1 and 0 by 42.1, we get a new number in which each digit is uniquely defined by corresponding digit of the original and the two digits closest to it. Application of F()
is equivalent to choosing new value for each digit based on its neighbors, and the definition of f()
above is nothing more than the transition table for rule 110.
Of course, this isn't a real proof, but I hope this sketch makes it clear where the undecidability comes from.
Important lines:
$curuser = $user['name']; // grabbing the current username and putting it into a variable
iterate function, included in home.php // iterates the directory and adds a button redirecting to delete.php where I want to write a delete/unlink function for the file.
delete.php is supposed to look somewhat like this:
$path = '$curuser/$file';
if (!unlink($path)) {
echo "Error";
} else {
header("Location: home.php");
Basically saying if I click "delete" it will delete the image and redirect me back to the original place immediately.
Which obviously doesn't work because if I iterate through all the files I don't store $file anywhere.
Can I somehow grab the link next to my delete button when I click delete?
Can I do it all in the iterate function?
Kinda lost here. I just want to delete files =(
*update: x starts as identityFunc (aka (iota iota)) not iota
Empty string is said to be identityFunc. Then append 0 or 1 to either call iota on you or call you on iota, then append again and so on to infinity.
I prefer models which can look into the left and right child of a halted function instead of having to call that function to detect what it does, which you may do either but calling a function which you dont know what it is seems risky of nonhalting vs emulating it n steps forward for some chosen n. Of course iota can derive any other universal lambda function which would only be called on combos of itself to use that universality most simply. This always calling 1 deeper is harder to understand than being able to call any combo of iota on any combo of iota like can be done in (slight derivation from s and k) Unlambda and Iota languages. If the thread title is true then it might be the simplest theory as from every possible state (each Lightcone is such a state?) theres 2 possible paths yet it contains all possible patterns.
>An elementary function is a function of one variable which is the composition of a finite number of arithmetic operations (+ β Γ Γ·), exponentials, logarithms, constants, trigonometric functions, and solutions of algebraic equations (a generalization of nth roots)
In other words, show that no matter how many times you repeatedly integrate ln(x), you still get a nice function.
Hint: >!Induction!<
If f(f(x))=x^(2)+1 find an f(x), preferably closed form. (Idk what kind of math this is.)
In a misogynistic family, the mother has already accepted the brainwashing. She's given birth, she's got a lower-value job (if at all), she's filled with internalised misogyny, and she's probably unable to escape now even if she wanted to. Reflection on her quality of life in this situation is too hard, so she ensures that her own experience is duplicated for her daughter. Then she'll have someone to either commiserate with, or to sneer at in order to feel good. Once her daughter is fully trained to be a chef/nurse/psychologist/secretary then she can finally relax, and while daughter is still in training she can take out her suppressed anger and anxiety on her. This is her reward for having been "a good woman".
In order that the family remain in the bubble, the daughter must agree to take care of mother, father, and brother because the mother's energy is waning after a lifetime of being dragged down, and she needs someone to take over the mantle of filling in the gaping gaps that the father and brother leave in the reality of the world (the superior beings can't seem to do much that even warrants respect, let alone warrants being almost worshipped in the form of being served daily, but surely we must persist in serving them... because? Because... we musn't ask questions.)
The daughter is treated as less than and still must be loving, eager, and giving towards her father and to her brothers, despite not wanting to do so. Again, filling in of gaps so that they don't have to feel any way at all, nor have to self-reflect on their behaviour.
The daughter holds a certain amount of social power, despite the fact that when she says no and chooses herself, she ends up attacked, demonised, scorned, insulted, and more by nearly everyone in her family. Because she has been trained to fill in the gaps to make everyone feel good throughout her entire existence, if she doesn't do that anymore she makes can make them feel very bad.
A daughter with low self-esteem is the linchpin everything rests on. If she breaks the chain even imperfectly, it still has an impact on changing the way things are in the world:
This question has probably screwed up the average score of my entire class:
Prove that if [; f'(z_0) ;] exists then [; f'(z_0) = \frac{df}{dx}(z_0) ;]
The proof that I gave, which was, as it turns out, was similar to some of my classmates, was something like:
[; f'(z_0) = \lim_{z \to z_0} \frac{ f(z) - f(z_0) }{ z - z_0 } ;]
[; = \lim_{x \to x_0, y \to y_0} \frac{ f(x, y) - f(x_0, y_0) }{ (x - x_0) + i(y + y_0) } ;]
[; = \lim_{x \to x_0} \lim_{y \to y_0} \frac{ f(x, y) - f(x_0, y_0) }{ (x - x_0) + i(y + y_0) } ;]
[; = \lim_{x \to x_0} \frac{ f(x, y_0) - f(x_0, y_0) }{ (x - x_0) } ;]
[; = \frac{df}{dx}(z_0) ;]
Now, notice that in the third step of the proof, I take [; \lim_{x \to x_0, y \to y_0} ;] to mean [; \lim_{x \to x_0} \lim_{ y \to y_0} ;].
My professor seems to think that if I let y go to y_0, that somehow means that I've chosen x as well, and therefore, letting y go to y_0 is not a valid step. In other words, that step would imply that f is continuous everywhere.
But what he seems to be confused about, is that continuity in the complex plane does not depend on the path. So I should be able to choose a path that happens to take y to y_0 first, and secondly x to x_0.
It seems many people in the class got this wrong, and had similar proofs. I tried convincing my prof twice, and got shot down twice. I'll give it one last shot, but I'm not sure how to shake his misconception.
Anyone have any ideas?
What's up, pals?
Decentralization and artificial intelligence have been recent themes. You are aware that you will not refute that reality. They are not just trends, but also topics that are often debated and commented on. Businesses are attempting to incorporate AI into their apps, even in their most basic forms. However, it is quite beneficial! It automates most procedures that formerly required human intervention.
WHO's information is out of date. We have the ability to notice what is going on around us. Diseases, crises, and poverty are not the only issues. They have a direct impact on our lives and behaviors. We've been through a lot in the last two years, and it's still going on. That is a worldwide sickness, not an individual one. Humanity must understand that decentralization is one of the best methods to relieve people's burdens. DeHealth is currently a trend that will, at the very least, infiltrate the global market.
DeHealth is an online patient registration platform that combines digital medical data storage with a cloud service. DeHealth enables you to save, manage, and protect personal health data while also offering quick access to all services provided by various medical institutions, both public and private. DeHealth users have topped 2.7 million to date, and the figure is continually increasing. The effort saves lives by supporting hundreds of thousands of people worldwide in resolving health difficulties. It is a really easy way to prevent unnecessary doctor visits, encounters with contaminated persons, and so forth.
I hope that such businesses aren't just a passing fad. Believe they have a real intention to help and give the world an opportunity to evolve further even in crisis.
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