Soul windsurfer

My home page - dead link,

Welcome!

Hello, Soul windsurfer, and welcome to Wikipedia! Thank you for your contributions. I hope you like the place and decide to stay. Here are some pages that you might find helpful:

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And don't forget, the edit summary is your friend. :) – Oleg Alexandrov (talk) 02:18, 15 May 2007 (UTC)

unblock

Your username hasn't been blocked, you maybe caught up by the block of the IP which you may share with other users or similarly an autoblock. We can't see anymore information and we don't mind read, so without you giving the full details of the block as shown on the block page it isn't possile to do anything to remove the block. --pgk^(talk) 22:22, 11 April 2006 (UTC)

Ths IP address in question is an open proxy. These are often used for vandalism, and this particular IP address was indeed used for vandalism about a month ago and was indefinitely blocked. Perhaps you can contact your network administrators or ISP and ask them to make the network more secure. -- Curps 05:15, 17 April 2006 (UTC)

Hi,

I answered your question on my talk page. The programs there are old and obsolete, and were never meant for general public usage. I'm don't want to write documentation for them. linas 22:15, 30 March 2007 (UTC)

Mandelbrot lemniscates

Adam, the definition of the lemniscates seems to vary. I've found sources on line that define the lemniscates with an escape radius, or with 1. I think we need to be clear whose definiition we are using, by giving a source for the information in the paragraph. From a mathematical point of view (as opposed to a computational one), I prefer 1, since we can define the mandelbrot set as the limit of the sequence of lemniscates with 1: there is no need to use any other threshold to define the set. By using the EscapeRadius, we will have a different sequence for each value of EscapeRadius. Not that there's anything wrong with that, simply that we don't need it. I'll try to find a good source for this today. Cheers, Doctormatt 16:34, 19 April 2007 (UTC)

Doctormatt, here are my source for Abs(Zn)=EscapeRadius :
| Wolfram
other source ( I think that it is wrong definition) :
2D curves
Cheers, (Adam majewski 17:30, 19 April 2007 (UTC))

escape radius

synonims:
bailout value = escape radius = the threshold radius
value:
r(c) = max(|c|,2)

Br tag

Hi Adam. Just a note. There is no need to insert a <br> tag on Wikipedia. You can just hit "return" twice to go to a new paragraph.

And one more note, math notation should be in math tags, so <math>f(x)</math> instead of simply f(x). Cheers, Oleg Alexandrov (talk) 02:19, 15 May 2007 (UTC)

I'd also suggest you learn the existing style on Wikipedia. Your change to Classification of Fatou components made it hard to read. Oleg Alexandrov (talk) 02:22, 15 May 2007 (UTC)

Re:Fatou components

I replied on my talk page. Cheers, Oleg Alexandrov (talk) 01:23, 16 May 2007 (UTC)

Translation

Do you take requests for translations? I would love the information on this page pl:Jan Krzysztof Kluk to be in this page Jan Krzysztof Kluk. Pro bug catcher (talk • contribs). 00:57, 22 April 2008 (UTC) Usually no, but I will try do do it ( :-)) --Adam majewski (talk) 16:32, 22 April 2008 (UTC)

Yes I'd be really happy to do what you proposed on my talk page. Pro bug catcher (talk • contribs). 11:25, 25 April 2008 (UTC)

Cardioid VS. Heart Shape

You asked for the heart shape expressed mathematically. Here's what I found: [1].

Although cardioids are heart-shaped, heart-shapes are not always cardioid. Make sense?

Also that is a very cool picture. Did you do it yourself? chad. (talk) 18:59, 7 December 2008 (UTC)

• Thx for good link.
• Yes, it makes sense.
• I'm not the author of picture, after permission I have downloaded it because I also like it. (:-))
• I have askeded question on page Reference desk --Adam majewski (talk) 16:28, 9 December 2008 (UTC)

Mandelbrot Set

Copied from the Mandelbrot Set talk page:

---

What are the extreme values of the real and imaginary components of the points contained in the set? Lucas Brown (talk) 02:25, 22 March 2009 (UTC)

Do you mean root point and apex point ?

Informations about boundaries of hyperbolic components :

boundaries computed with boundary equations

boundaries computed with Newton Method

--Adam majewski (talk) 06:59, 22 March 2009 (UTC)

---

What do you mean by "root point" and "apex point?" Lucas Brown (talk) 18:12, 27 March 2009 (UTC) I have answered on the Mandelbrot Set talk page. --Adam majewski (talk) 09:17, 28 March 2009 (UTC)

I was wondering...

About the mandelbrot curves above , what function f(x,y) = 0 was used to statisfy this curve ? This function was used to plot the those graph I assume . I can only guess this function was a power series of x and y. —Preceding unsigned comment added by Z E U S (talk • contribs) 00:09, 11 June 2009 (UTC) Hi. Thx for question. For example :

• boundary of large central figure ( period 1 hyperbolic component) is a cardioid with equation :

$c={\frac {e^{it}}{2}}-\left({\frac {e^{it}}{2}}\right)^{2}\,$

• second largest cardioid is boundary of period 3 component on main antennae,

$c=\left({\frac {(P-1){\sqrt {27P^{2}-22P+23}}}{6{\sqrt {3}}}}-{\frac {27P^{2}-36P+25}{54}}\right)^{1/3}+{\frac {3P+1}{9\left({\frac {(P-1){\sqrt {27P^{2}-22P+23}}}{6{\sqrt {3}}}}-{\frac {27P^{2}-36P+25}{54}}\right)^{1/3}}}-{\frac {2}{3}}\,$

For other curves see:

• boundary equations up to period 7 ( 8). These are implicit functions.

For higher periods functions are not in form of equation. Only some points are computed.

• book about solving boundary equations

HTH

--Adam majewski (talk) 21:04, 14 June 2009 (UTC)

(pre)periodic pts versus Misiurewicz points

Thanks for taking the time to change the internal link on the Arithmetic Dynamics page, but I'm going to revert back to the old version. Periodic and preperiodic points are not the same as Misiurewicz points. They don't live in the same spaces. For example, the Misiurewicz points for the polynomial x^2+c are the c-values for which the critical point x=0 is preperiodic. JosephSilverman (talk) 15:54, 12 July 2009 (UTC)

I know it ( z points of dynamical plane and c points of parameter plane). It is in the first statement of this article, I thought that it will be better link , but ... Are you an author of "The Arithmetic of Dynamical Systems" ?

Yep, that's me. JosephSilverman (talk) 20:30, 15 July 2009 (UTC)

Hi Adam, thanks for your note. Unfortunately, at present I have a very limited amount of time that I can spend on wikipedia. So for now I'm going to concentrate on working on the topics that I've listed on my home page. Someday, if/when I have more time, I'll get more involved with checking things more widely within mathematics. JosephSilverman (talk) 14:42, 18 July 2009 (UTC)

Hi, Joseph. Thx for your answer. --Adam majewski (talk) 17:46, 18 July 2009 (UTC)

File:Demj

The ANSI C standard specifies exactly two possible function signatures. int foo() in C denotes an "unspecified [=any] number of arguments", which is not the same as int foo(void) (exactly zero arguments). —j.eng (talk) 01:24, 5 November 2009 (UTC)

Mandelbrot set

Can you explain your latest edit to this article? How does the topological model of the Mandelbrot set relate to its local connectivity? :| TelCoNaSpVe :| 21:42, 30 June 2010 (UTC)

I'm not sure but I supose that this topological model is equal to "pinched disk" model. --Adam majewski (talk) 14:02, 1 July 2010 (UTC) " ... the homeomorphism between the model and the boundary of the M-set depends on the local connectivity conjecture " RDBury

Alright, I want to make sure that the image was relevant to the article; otherwise it could be deleted. By the way, you could help with cleaning up the article by mentioning what pictures there are to remove and what pictures there are to remain on the talk page of the article. :| TelCoNaSpVe :| 16:07, 1 July 2010 (UTC)

Apollonian gasket

Thanks for your question about File:Apollonian gasket.svg - yes, if you take all circles within the 20 levels/steps you get about 3^21 circles in all; but of course such a huge file couldn't be uploaded to commons and took a long time to render on a reasonably fast machine. Reducing the number of levels produced some ugly holes with no circles in at all, particularly around the edges where the three large circles touch the very large outer circle. Eventually I decided to modify the program so it would stop when it got to a certain radius of circle rather than going through a certain number of levels. I probably still have the code somewhere - let me know if you'd like to see it. Time3000 (talk) 16:29, 4 September 2010 (UTC)

Thx. For answer. I would like to see code. --Adam majewski (talk) 20:16, 4 September 2010 (UTC)

I'll try to find it at some point - it's not on my usual computer, so it might be a few days. Time3000 (talk) 20:40, 5 September 2010 (UTC)

DNA and Arc

I removed the info about the decipherment using Arc, because (a) there doesn't seem to be anything very specific to Arc that makes this possible; (b) 30 people had done this before him without Arc, so what is special about this case?; (c) it doesn't seem to add anything useful to the Arc article. Should every programming language article report on the first time some particular problem has been attacked with it? (Headlines: "C# used for microwave oven controller"; "Pi calculated to 100,000 places using R"; etc.) --Macrakis (talk) 19:01, 9 September 2010 (UTC)

Re: Sand drawings

Hi Adam, sorry for the delayed answer. Yes, I think there are two options: Either the title is changed to something like "Sand drawings (Vanuatu)" or maybe "Sandroings" or the article could be expanded to include similar practices around the world. From a long-term perspective, the latter option might be more attractive, I think. Cheers, Watasenia (talk) —Preceding undated comment added 10:28, 20 November 2010 (UTC).

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File:Dotswirl.gif

Sorry, I made this several years ago and do not remember the parameters I used. --❨Ṩtruthious ℬandersnatch❩ 20:33, 18 April 2012 (UTC)

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About derivatives...

To clear it up:

Univariable functions, ordinary derivatives

For a function of one variable, y = y(x), only ordinary derivatives are needed.

• The notation ${\dfrac {dy(x)}{dx}}$ means find the derivative of y with respect to x, using the differentiation rules.

• Depending on the context, it could also mean the ratio of two differentials, the differential in y (written dy) divided by the differential in x (written dx), but for first order derivatives the ratio of two differentials and the first order derivative happen to coincide:

${\underset {\text{differential}}{dy}}={\underset {\text{derivative}}{\frac {dy}{dx}}}{\underset {\text{differential}}{dx}}\quad \Rightarrow \quad {\underset {\text{ratio of differentials}}{\dfrac {dy}{dx}}}={\underset {\text{derivative}}{\dfrac {dy}{dx}}}$

• (Note the terms "differentiate" mean to "find the derivative").
• Put another way, the symbol for an ordinary derivative, ${\dfrac {d\cdots }{d\cdots }}$, is a single symbol, while in a ratio of two differentials, the "dy" and "dx" can be separated.

To substitute values:

• The notation $\left.{\dfrac {dy(x)}{dx}}\right|_{x=a}$ or ${\dfrac {dy(a)}{dx}}$ mean to find the derivative of y with respect to x, using the differentiation rules, then substitute x = a (where a is a constant) into the result. If you were to substitute x = a into the function y = y(a) first, then y(a) is a constant as the variable x would be eliminated, and the derivative is zero.
• The notation ${\dfrac {d}{dx}}y(a)$ usually means the same thing by convention, but it could also mean that x = a is substituted into y = y(x), then differentiated, which only gives zero...

Since the derivative of a function (if it exists) is another function, some people also write:

${\dfrac {dy}{dx}}(x)$ or $\left({\dfrac {dy}{dx}}\right)(x)$

then the derivative evaluated at a point x = a is written as for functions:

${\dfrac {dy}{dx}}(a)$ or $\left({\dfrac {dy}{dx}}\right)(a)$

All this is Leibniz's notation. Newton's notation uses one dot over the y for each derivative with respect to x (this is especially used in the context of mechanics, when quantities are differentiated with respect to time). Lagrange's notation uses one prime on y for each derivative with respect to x.

Multivariable functions, partial derivatives

For a function of more than one variable, f = f(x, y, z, ...), partial derivatives are used. A partial derivative with respect to any one variable follows exactly the same differentiation rules as for ordinary derivatives, just keep the other variables constant. For example if:

$f(x,y,z)=x^{p}y^{q}z^{r}+e^{y}-\sin(z)$

where p, q, r are constants, then:

${\dfrac {\partial f(x,y,z)}{\partial x}}=px^{p-1}y^{q}z^{r}$

${\dfrac {\partial f(x,y,z)}{\partial y}}=x^{p}qy^{q-1}z^{r}+e^{y}$

${\dfrac {\partial f(x,y,z)}{\partial z}}=x^{p}y^{q}rz^{r-1}-\cos(z)$

Yet another notational convention is to use brackets and subscript the variables kept constant:

${\dfrac {\partial f}{\partial x}}=\left({\dfrac {\partial f}{\partial x}}\right)_{y,z}\,,{\dfrac {\partial f}{\partial y}}=\left({\dfrac {\partial f}{\partial y}}\right)_{x,z}\,,\,{\dfrac {\partial f}{\partial z}}=\left({\dfrac {\partial f}{\partial z}}\right)_{x,y}\,.$

• You can differentiate with respect to one variable, then another, and another, etc., for example:

${\dfrac {\partial f}{\partial x}}\,,\quad {\dfrac {\partial ^{2}f}{\partial z^{2}}}\,,\quad {\dfrac {\partial ^{2}f}{\partial z\partial x}}\,,\quad {\dfrac {\partial ^{3}f}{\partial x\partial y\partial z}}\,,\quad {\dfrac {\partial ^{3}f}{\partial x\partial y^{2}}}\,,\cdots \,,{\dfrac {\partial ^{15}f}{\partial y^{6}\partial z^{9}}}\,,\cdots$

which are respectively first order, second order, second order, third order, third order, ..., fifteenth order, ... partial derivatives of f (assuming they exist). Yes, they are called mixed partial derivatives when there is more than one variable differentiated. See also symmetry of second derivatives.

• The notation for substituting numbers applies to each variable, and is similar to the notation for ordinary derivatives as above, e.g. to differentiate y with respect to x, then substitute only z = a (constant), we write:

$\left.{\dfrac {\partial f(x,y,z,\ldots )}{\partial x}}\right|_{z=a}$ or simply $\left.{\dfrac {\partial f}{\partial x}}\right|_{z=a}$ or ${\dfrac {\partial f(x,y,a,\ldots )}{\partial x}}$

• The first order partial derivative of f with respect to any one variable,

${\dfrac {\partial f}{\partial x}},\quad {\dfrac {\partial f}{\partial y}},\quad {\dfrac {\partial f}{\partial z}},\,\cdots$

is not simply a ratio of two differentials, so there is no ambiguity as with ordinary derivatives. The symbol for a partial derivative, ${\dfrac {\partial \cdots }{\partial \cdots }}$, is a single symbol: the $\partial \cdots$ in the "numerator" is not to be separated from the $\partial \cdots$ in the "denominator", and expressions $\partial f$ or $\partial x$ like that alone are not meaningful. The total differential of f is defined as:

$df={\dfrac {\partial f}{\partial x}}dx+{\dfrac {\partial f}{\partial y}}dy+{\dfrac {\partial f}{\partial z}}dz+\cdots$

where df, dx, dy, dz, etc., are all differentials. You can divide by any one of these throughout, say dy, to find:

${\dfrac {df}{dy}}={\dfrac {\partial f}{\partial x}}{\dfrac {dx}{dy}}+{\dfrac {\partial f}{\partial y}}+{\dfrac {\partial f}{\partial z}}{\dfrac {dz}{dy}}+\cdots$

Hope this and the article on notation for differentiation helps. In case you have difficulties, please refer to a calculus text, the Schaum's Outlines books are really good (and affordable!). Best, M∧Ŝc²ħεИ_τlk 18:20, 14 January 2014 (UTC)

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Re: Near-copies of the Mandelbrot set within itself

Hi, Adam, I have added coordinates to my images in this category. Aokoroko (talk) 22:22, 20 April 2017 (UTC)

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Mandelbrot Interior Detection

Hey there, I saw your image on a wikibook https://commons.wikimedia.org/wiki/File:Mandelbrot_set_with_Interior_detection_method.png

And i was trying to achieve a result like the image you posted. I have quite a different setup as what you use to render it, so i couldn't quite grasp my head around it.

Right now i can detect whether the point is inside the set using cabs(d) < eps. But from there, how can i color the points based on the distance?

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Hi answered your question on 1D torus

Hi Adam, answered your question on Talk:Torus. (you know me, I'm just working anonymously, here). 67.198.37.16 (talk) 07:00, 20 December 2018 (UTC)

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Thank you. Leschnei (talk) 00:54, 14 November 2019 (UTC)

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I have removed the copied text as it was unsourced and largely incorrect. PaulT2022 (talk) 21:53, 2 December 2022 (UTC)

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