Re: Fractal Dimension Computation in Python Code

2019-05-02 Thread tiwari . ram77
On Friday, September 29, 2000 at 12:45:00 PM UTC+5:45, Mike Brenner wrote: > Myk> ... Has anyone got a fast routine for calculating the fractal > dimension of a set of points in 2 or 3D space? Thanks. > > According to the inventor of fractals (Hausdorff in the year 1899), you >

Re: Writing a program to illustrate a fractal

2018-08-26 Thread Richard Damon
On 8/26/18 5:40 PM, Dennis Lee Bieber wrote: > But their definition is still confusing as it is formulated with a > expression as the argument to a(). > > Taken literally, it says for n+4 to call a() with an argument of 8 (2n) > AND to call it with an argument of 7 (2n-1) (returning

Re: Writing a program to illustrate a fractal

2018-08-26 Thread Musatov
On Sunday, August 26, 2018 at 3:13:00 PM UTC-5, Oscar Benjamin wrote: > On Sun, 26 Aug 2018 at 20:52, Musatov wrote: > > > > Thank you, Richard. If anyone is interested further, even in writing a > > Python code to generate the sequence or further preparing of an animation I > > would be

Re: Writing a program to illustrate a fractal

2018-08-26 Thread Oscar Benjamin
On Sun, 26 Aug 2018 at 20:52, Musatov wrote: > > Thank you, Richard. If anyone is interested further, even in writing a Python > code to generate the sequence or further preparing of an animation I would be > delighted. It would not take long to write code to plot your sequence if you first

Re: Writing a program to illustrate a fractal

2018-08-26 Thread Musatov
by: > >>>> > >>>> For 1 <= n <= 3, a(n) = n; thereafter, a(2n) = a(n) + a(n+1), a(2n-1) = > >>>> a(n) + a(n-2). > > >>> I am not sure what 'fractal' property this sequence has that he > >>> wants to > >> display

Re: Writing a program to illustrate a fractal

2018-08-26 Thread Richard Damon
(n) + a(n+1), a(2n-1) = >>>> a(n) + a(n-2). >>> I am not sure what 'fractal' property this sequence has that he >>> wants to >> display. > I'm sorry, let me try to explain: > > Here is my output: > 1, 2, 3, 5, 4, 8, 7, 9, 7, 12, 13, 15, 11, 16, 17

Re: Writing a program to illustrate a fractal

2018-08-26 Thread Musatov
o, it is not a strict function. I'd also write it > > as > > I think they intend that a(n) is defined for n being an integer (or > maybe just the Natural Numbers, since it isn't defined for values below 1) > > The two provided definitions provide the recursive definition for e

Re: Writing a program to illustrate a fractal

2018-08-26 Thread Richard Damon
t;=4 you are > returning TWO values? If so, it is not a strict function. I'd also write it > as I think they intend that a(n) is defined for n being an integer (or maybe just the Natural Numbers, since it isn't defined for values below 1) The two provided definitions provide the recursive definition for e

Writing a program to illustrate a fractal

2018-08-26 Thread Musatov
I have an integer sequence of a fractal nature and want to know if it is possible to write a program to illustrate it in a manner similar to the many animated Mandelbrot illustrations. The sequence is defined by: For 1 <= n <= 3, a(n) = n; thereafter, a(2n) = a(n) + a(n+1), a(2n-1)

Re: Fractal

2013-05-16 Thread Ulrich Eckhardt
Am 16.05.2013 02:00, schrieb alex23: My favourite is this one: http://preshing.com/20110926/high-resolution-mandelbrot-in-obfuscated-python Not only is this blog entry an interesting piece of art, there's other interesting things to read there, too. Thanks! Uli --

Re: Fractal

2013-05-16 Thread Chris Angelico
On Thu, May 16, 2013 at 5:11 PM, Ulrich Eckhardt ulrich.eckha...@dominolaser.com wrote: Am 16.05.2013 02:00, schrieb alex23: My favourite is this one: http://preshing.com/20110926/high-resolution-mandelbrot-in-obfuscated-python Not only is this blog entry an interesting piece of art,

Re: Fractal

2013-05-16 Thread Ian Kelly
On Thu, May 16, 2013 at 5:04 AM, Sharon COUKA sharon_co...@hotmail.com wrote: I have to write the script, and i have one but the zoom does not work That doesn't answer my question. Perhaps if you would share with us what you already have, then we could point out what you need to do and where to

Re: Fractal

2013-05-16 Thread Ian Kelly
On Thu, May 16, 2013 at 10:55 AM, Sharon COUKA sharon_co...@hotmail.com wrote: # Register events c.bind('i', zoom) c.bind('i', unzoom) c.bind('i', mouseMove) I'm not an expert at Tkinter so maybe one of the other residents can help you better with that. The code above looks wrong to me,

Fractal

2013-05-15 Thread Sharon COUKA
Hello, I'm new to python and i have to make a Mandelbrot fractal image for school but I don't know how to zoom in my image. Thank you for helping me. Envoyé de mon iPad -- http://mail.python.org/mailman/listinfo/python-list

Re: Fractal

2013-05-15 Thread Colin J. Williams
On 13/05/2013 11:41 AM, Sharon COUKA wrote: Hello, I'm new to python and i have to make a Mandelbrot fractal image for school but I don't know how to zoom in my image. Thank you for helping me. Envoyé de mon iPad Google is your friend. Try Mandelbrot Python Colin W. -- http

Re: Fractal

2013-05-15 Thread Grant Edwards
On 2013-05-13, Sharon COUKA sharon_co...@hotmail.com wrote: Hello, I'm new to python and i have to make a Mandelbrot fractal image for school but I don't know how to zoom in my image. Thank you for helping me. It's a fractal image, so you zoom in/out with the following Python instruction

Re: Fractal

2013-05-15 Thread Ian Kelly
On Mon, May 13, 2013 at 9:41 AM, Sharon COUKA sharon_co...@hotmail.com wrote: Hello, I'm new to python and i have to make a Mandelbrot fractal image for school but I don't know how to zoom in my image. Thank you for helping me. Is this a GUI application or does it just write the image

Re: Fractal

2013-05-15 Thread alex23
On May 15, 10:07 pm, Colin J. Williams c...@ncf.ca wrote: Google is your friend.  Try Mandelbrot Python My favourite is this one: http://preshing.com/20110926/high-resolution-mandelbrot-in-obfuscated-python -- http://mail.python.org/mailman/listinfo/python-list

Re: Measuring Fractal Dimension ?

2009-06-30 Thread pdpi
On Jun 29, 3:17 am, greg g...@cosc.canterbury.ac.nz wrote: Paul Rubin wrote: Steven D'Aprano st...@remove-this-cybersource.com.au writes: But that depends on what you call things... if electron shells are real (and they seem to be) and discontinuous, and the shells are predicted/ specified

Re: Measuring Fractal Dimension ?

2009-06-28 Thread Steven D'Aprano
On Thu, 25 Jun 2009 12:23:07 +0100, Robin Becker wrote: Paul Rubin wrote: [...] No really, it is just set theory, which is a pretty bogus subject in some sense. There aren't many discontinuous functions in nature. Depends on how you define discontinuous. Catastrophe theory is full of

Re: Measuring Fractal Dimension ?

2009-06-28 Thread Paul Rubin
Steven D'Aprano st...@remove-this-cybersource.com.au writes: Depends on how you define discontinuous. The mathematical way, of course. For any epsilon 0, etc. Catastrophe theory is full of discontinuous changes in state. Animal (by which I include human) behaviour often displays

Re: Measuring Fractal Dimension ?

2009-06-28 Thread Steven D'Aprano
On Sat, 27 Jun 2009 23:52:02 -0700, Paul Rubin wrote: Steven D'Aprano st...@remove-this-cybersource.com.au writes: Depends on how you define discontinuous. The mathematical way, of course. For any epsilon 0, etc. I thought we were talking about discontinuities in *nature*, not in

Re: Measuring Fractal Dimension ?

2009-06-28 Thread Paul Rubin
Steven D'Aprano st...@remove-this-cybersource.com.au writes: I thought we were talking about discontinuities in *nature*, not in mathematics. There's no of course about it. IIRC we were talking about fractals, which are a topic in mathematics. This led to some discussion of mathematical

Re: Measuring Fractal Dimension ?

2009-06-28 Thread Steven D'Aprano
On Sun, 28 Jun 2009 03:28:51 -0700, Paul Rubin wrote: Steven D'Aprano st...@remove-this-cybersource.com.au writes: I thought we were talking about discontinuities in *nature*, not in mathematics. There's no of course about it. IIRC we were talking about fractals, which are a topic in

Re: Measuring Fractal Dimension ?

2009-06-28 Thread Paul Rubin
Steven D'Aprano st...@remove-this-cybersource.com.au writes: But that depends on what you call things... if electron shells are real (and they seem to be) and discontinuous, and the shells are predicted/ specified by eigenvalues of some continuous function, is the continuous function part of

Re: Measuring Fractal Dimension ?

2009-06-28 Thread greg
Steven D'Aprano wrote: one minute the grenade is sitting there, stable as can be, the next it's an expanding cloud of gas and metal fragments. I'm not sure that counts as discontinuous in the mathematical sense. If you were to film the grenade exploding and play it back slowly enough, the

Re: Measuring Fractal Dimension ?

2009-06-28 Thread greg
Paul Rubin wrote: Steven D'Aprano st...@remove-this-cybersource.com.au writes: But that depends on what you call things... if electron shells are real (and they seem to be) and discontinuous, and the shells are predicted/ specified by eigenvalues of some continuous function, is the continuous

Re: Measuring Fractal Dimension ?

2009-06-28 Thread Terry Reedy
greg wrote: Steven D'Aprano wrote: one minute the grenade is sitting there, stable as can be, the next it's an expanding cloud of gas and metal fragments. I'm not sure that counts as discontinuous in the mathematical sense. If you were to film the grenade exploding and play it back slowly

Re: Measuring Fractal Dimension ?

2009-06-27 Thread Paul Rubin
Robin Becker ro...@reportlab.com writes: There is a philosophy of mathematics (intuitionism) that says... there are NO discontinuous functions. so does this render all the discreteness implied by quantum theory unreliable? or is it that we just cannot see(measure) the continuity that

Re: Measuring Fractal Dimension ?

2009-06-25 Thread Robin Becker
pdpi wrote: ... But yeah, Log2 and LogE are the only two bases that make natural sense except in specialized contexts. Base 10 (and, therefore, Log10) is an artifact of having that 10 fingers (in fact, whatever base you use, you always refer to it as base 10). someone once explained to me

Re: Measuring Fractal Dimension ?

2009-06-25 Thread Paul Rubin
Robin Becker ro...@reportlab.com writes: someone once explained to me that the set of systems that are continuous in the calculus sense was of measure zero in the set of all systems I think it was a fairly formal discussion, but my understanding was of the hand waving sort. That is very

Re: Measuring Fractal Dimension ?

2009-06-25 Thread Robin Becker
Paul Rubin wrote: . That is very straightforward if you don't mind a handwave. Let S be some arbitrary subset of the reals, and let f(x)=0 if x is in S, and 1 otherwise (this is a discontinuous function if S is nonempty). How many different such f's can there be? Obviously one for

Re: Measuring Fractal Dimension ?

2009-06-25 Thread pdpi
On Jun 25, 12:23 pm, Robin Becker ro...@reportlab.com wrote: Paul Rubin wrote: so does this render all the discreteness implied by quantum theory unreliable? or is it that we just cannot see(measure) the continuity that really happens? Certainly there are people like Wolfram who seem to think

Re: Measuring Fractal Dimension ?

2009-06-25 Thread pdpi
On Jun 25, 10:38 am, Paul Rubin http://phr...@nospam.invalid wrote: Robin Becker ro...@reportlab.com writes: someone once explained to me that the set of systems that are continuous in the calculus sense was of measure zero in the set of all systems I think it was a fairly formal

Re: Measuring Fractal Dimension ?

2009-06-24 Thread Mark Dickinson
On Jun 24, 10:12 am, pdpi pdpinhe...@gmail.com wrote: Regarding inf ** 0, why does IEEE745 define it as 1, when there is a perfectly fine NaN value? Have a look at: http://www.eecs.berkeley.edu/~wkahan/ieee754status/ieee754.ps (see particularly page 9). Mark --

Re: Measuring Fractal Dimension ?

2009-06-24 Thread Steven D'Aprano
On Mon, 22 Jun 2009 13:43:19 -0500, David C. Ullrich wrote: In my universe the standard definition of log is different froim what log means in a calculus class Now I'm curious what the difference is. -- Steven -- http://mail.python.org/mailman/listinfo/python-list

Re: Measuring Fractal Dimension ?

2009-06-24 Thread Mark Dickinson
On Jun 24, 10:12 am, pdpi pdpinhe...@gmail.com wrote: Regarding inf ** 0, why does IEEE745 define it as 1, when there is a perfectly fine NaN value? Other links: the IEEE 754 revision working group mailing list archives are public; there was extensive discussion about special values of pow

Re: Measuring Fractal Dimension ?

2009-06-24 Thread Hendrik van Rooyen
Steven D'Aprano ste...@remove.this.c...com.au wrote: On Mon, 22 Jun 2009 13:43:19 -0500, David C. Ullrich wrote: In my universe the standard definition of log is different froim what log means in a calculus class Now I'm curious what the difference is. Maybe he is a lumberjack, and quite

Re: Measuring Fractal Dimension ?

2009-06-24 Thread pdpi
On Jun 24, 2:58 pm, Hendrik van Rooyen m...@microcorp.co.za wrote: Steven D'Aprano ste...@remove.this.c...com.au wrote: On Mon, 22 Jun 2009 13:43:19 -0500, David C. Ullrich wrote: In my universe the standard definition of log is different froim what log means in a calculus class Now I'm

Re: Measuring Fractal Dimension ?

2009-06-24 Thread pdpi
On Jun 24, 1:32 pm, Mark Dickinson dicki...@gmail.com wrote: On Jun 24, 10:12 am, pdpi pdpinhe...@gmail.com wrote: Regarding inf ** 0, why does IEEE745 define it as 1, when there is a perfectly fine NaN value? Other links:  the IEEE 754 revision working group mailing list archives are

Re: Measuring Fractal Dimension ?

2009-06-23 Thread Mark Dickinson
On Jun 23, 3:52 am, Steven D'Aprano ste...@remove.this.cybersource.com.au wrote: On Mon, 22 Jun 2009 13:43:19 -0500, David C. Ullrich wrote: In my universe the standard definition of log is different froim what log means in a calculus class Now I'm curious what the difference is. It's just

Re: Measuring Fractal Dimension ?

2009-06-23 Thread Lie Ryan
Mark Dickinson wrote: On Jun 23, 3:52 am, Steven D'Aprano ste...@remove.this.cybersource.com.au wrote: On Mon, 22 Jun 2009 13:43:19 -0500, David C. Ullrich wrote: In my universe the standard definition of log is different froim what log means in a calculus class Now I'm curious what the

Re: Measuring Fractal Dimension ?

2009-06-23 Thread Aahz
In article b64766a2-fd6f-4aa9-945f-381c0692b...@w40g2000yqd.googlegroups.com, Mark Dickinson dicki...@gmail.com wrote: On Jun 22, 7:43=A0pm, David C. Ullrich ullr...@math.okstate.edu wrote: Surely you don't say a curve is a subset of the plane and also talk about the integrals of verctor

Re: Measuring Fractal Dimension ?

2009-06-22 Thread pdpi
of a continuous one-to-one function from R/Z to R2. [...] - Tom Hales, in 'Jordan's Proof of the Jordan Curve Theorem'. We say that Gamma is a curve if it is the image in the plane or in space of an interval [a, b] of real numbers of a continuous function gamma. - Claude Tricot, 'Curves and Fractal

Re: Measuring Fractal Dimension ?

2009-06-22 Thread Charles Yeomans
On Jun 22, 2009, at 8:46 AM, pdpi wrote: On Jun 19, 8:13 pm, Charles Yeomans char...@declaresub.com wrote: On Jun 19, 2009, at 2:43 PM, David C. Ullrich wrote: snick Hmm. You left out a bit in the first definition you cite: A simple closed curve J, also called a Jordan curve, is the

Re: Measuring Fractal Dimension ?

2009-06-22 Thread David C . Ullrich
numbers of a continuous function gamma. - Claude Tricot, 'Curves and Fractal Dimension' (Springer, 1995). Perhaps your definition of curve isn't as universal or 'official' as you seem to think it is? Perhaps not. I'm very surprised to see those definitions; I've been a mathematician for 25

Re: Measuring Fractal Dimension ?

2009-06-22 Thread David C . Ullrich
On Mon, 22 Jun 2009 10:31:26 -0400, Charles Yeomans char...@declaresub.com wrote: On Jun 22, 2009, at 8:46 AM, pdpi wrote: On Jun 19, 8:13 pm, Charles Yeomans char...@declaresub.com wrote: On Jun 19, 2009, at 2:43 PM, David C. Ullrich wrote: snick Hmm. You left out a bit in the first

Re: Measuring Fractal Dimension ?

2009-06-22 Thread David C . Ullrich
On Fri, 19 Jun 2009 12:40:36 -0700 (PDT), Mark Dickinson dicki...@gmail.com wrote: On Jun 19, 7:43 pm, David C. Ullrich ullr...@math.okstate.edu wrote: Evidently my posts are appearing, since I see replies. I guess the question of why I don't see the posts themselves \is ot here... Judging by

Re: Measuring Fractal Dimension ?

2009-06-22 Thread Mark Dickinson
On Jun 22, 7:43 pm, David C. Ullrich ullr...@math.okstate.edu wrote: Surely you don't say a curve is a subset of the plane and also talk about the integrals of verctor fields over _curves_? [snip rest of long response that needs a decent reply, but possibly not here... ] I wonder whether we

Re: Measuring Fractal Dimension ?

2009-06-22 Thread Charles Yeomans
On Jun 22, 2009, at 2:16 PM, David C. Ullrich wrote: On Mon, 22 Jun 2009 10:31:26 -0400, Charles Yeomans char...@declaresub.com wrote: On Jun 22, 2009, at 8:46 AM, pdpi wrote: On Jun 19, 8:13 pm, Charles Yeomans char...@declaresub.com wrote: On Jun 19, 2009, at 2:43 PM, David C. Ullrich

Re: Measuring Fractal Dimension ?

2009-06-19 Thread David C . Ullrich
in the plane or in space of an interval [a, b] of real numbers of a continuous function gamma. - Claude Tricot, 'Curves and Fractal Dimension' (Springer, 1995). Perhaps your definition of curve isn't as universal or 'official' as you seem to think it is? Perhaps not. I'm very surprised to see those

Re: Measuring Fractal Dimension ?

2009-06-19 Thread Charles Yeomans
'. We say that Gamma is a curve if it is the image in the plane or in space of an interval [a, b] of real numbers of a continuous function gamma. - Claude Tricot, 'Curves and Fractal Dimension' (Springer, 1995). Perhaps your definition of curve isn't as universal or 'official' as you seem to think

Re: Measuring Fractal Dimension ?

2009-06-19 Thread Mark Dickinson
On Jun 19, 7:43 pm, David C. Ullrich ullr...@math.okstate.edu wrote: Evidently my posts are appearing, since I see replies. I guess the question of why I don't see the posts themselves \is ot here... Judging by this thread, I'm not sure that much is off-topic here. :-) Perhaps not. I'm very

Re: Measuring Fractal Dimension ?

2009-06-19 Thread pdpi
On Jun 17, 1:26 pm, Jaime Fernandez del Rio jaime.f...@gmail.com wrote: P.S. The snowflake curve, on the other hand, is uniformly continuous, right? The definition of uniform continuity is that, for any epsilon 0, there is a delta 0 such that, for any x and y, if x-y delta, f(x)-f (y)

Re: Measuring Fractal Dimension ?

2009-06-19 Thread Paul Rubin
Mark Dickinson dicki...@gmail.com writes: It looks as though you're treating (a portion of?) the Koch curve as the graph of a function f from R - R and claiming that f is uniformly continuous. But the Koch curve isn't such a graph (it fails the 'vertical line test', I think you treat it as a

Re: Measuring Fractal Dimension ?

2009-06-19 Thread David C . Ullrich
On Wed, 17 Jun 2009 05:46:22 -0700 (PDT), Mark Dickinson dicki...@gmail.com wrote: On Jun 17, 1:26 pm, Jaime Fernandez del Rio jaime.f...@gmail.com wrote: On Wed, Jun 17, 2009 at 1:52 PM, Mark Dickinsondicki...@gmail.com wrote: Maybe James is thinking of the standard theorem that says that

Re: Measuring Fractal Dimension ?

2009-06-18 Thread David C . Ullrich
a fractal dimension. It's got to be uncountably infinite, and therefore uncomputable. I think the idea is you assume uniform continuity of the set (as expressed by a parametrized curve). That should let you approximate the fractal dimension. Fractals are, by definition, not uniform in that sense

Re: Measuring Fractal Dimension ?

2009-06-18 Thread David C . Ullrich
a fractal dimension. It's got to be uncountably infinite, and therefore uncomputable. I think the idea is you assume uniform continuity of the set (as expressed by a parametrized curve). That should let you approximate the fractal dimension. Fractals are, by definition, not uniform in that sense

Re: Measuring Fractal Dimension ?

2009-06-18 Thread David C . Ullrich
a fractal dimension. It's got to be uncountably infinite, and therefore uncomputable. I think the idea is you assume uniform continuity of the set (as expressed by a parametrized curve). That should let you approximate the fractal dimension. Fractals are, by definition, not uniform in that sense

Re: Measuring Fractal Dimension ?

2009-06-18 Thread David C . Ullrich
writes: I don't think any countable set, even a countably-infinite set, can have a fractal dimension. It's got to be uncountably infinite, and therefore uncomputable. I think the idea is you assume uniform continuity of the set (as expressed by a parametrized curve).  That should let you

Re: Measuring Fractal Dimension ?

2009-06-18 Thread David C . Ullrich
On Wed, 17 Jun 2009 07:37:32 -0400, Charles Yeomans char...@declaresub.com wrote: On Jun 17, 2009, at 2:04 AM, Paul Rubin wrote: Jaime Fernandez del Rio jaime.f...@gmail.com writes: I am pretty sure that a continuous sequence of curves that converges to a continuous curve, will do so

Re: Measuring Fractal Dimension ?

2009-06-18 Thread David C . Ullrich
On Wed, 17 Jun 2009 08:18:52 -0700 (PDT), Mark Dickinson dicki...@gmail.com wrote: On Jun 17, 3:46 pm, Paul Rubin http://phr...@nospam.invalid wrote: Mark Dickinson dicki...@gmail.com writes: It looks as though you're treating (a portion of?) the Koch curve as the graph of a function f from

Re: Measuring Fractal Dimension ?

2009-06-18 Thread Charles Yeomans
On Jun 18, 2009, at 2:19 PM, David C. Ullrich wrote: On Wed, 17 Jun 2009 07:37:32 -0400, Charles Yeomans char...@declaresub.com wrote: On Jun 17, 2009, at 2:04 AM, Paul Rubin wrote: Jaime Fernandez del Rio jaime.f...@gmail.com writes: I am pretty sure that a continuous sequence of curves

Re: Measuring Fractal Dimension ?

2009-06-18 Thread Arnaud Delobelle
David C. Ullrich ullr...@math.okstate.edu writes: On Wed, 17 Jun 2009 08:18:52 -0700 (PDT), Mark Dickinson dicki...@gmail.com wrote: On Jun 17, 3:46 pm, Paul Rubin http://phr...@nospam.invalid wrote: Mark Dickinson dicki...@gmail.com writes: It looks as though you're treating (a portion

Re: Measuring Fractal Dimension ?

2009-06-18 Thread Mark Dickinson
Proof of the Jordan Curve Theorem'. We say that Gamma is a curve if it is the image in the plane or in space of an interval [a, b] of real numbers of a continuous function gamma. - Claude Tricot, 'Curves and Fractal Dimension' (Springer, 1995). Perhaps your definition of curve isn't as universal

Re: Measuring Fractal Dimension ?

2009-06-18 Thread Paul Rubin
David C. Ullrich ullr...@math.okstate.edu writes: obviously converges to f, but not uniformly. On a closed interval, any continuous function is uniformly continuous. Isn't (-?, ?) closed? What is your version of the definition of closed? I think the whole line is closed, but I hadn't

Re: Measuring Fractal Dimension ?

2009-06-17 Thread Paul Rubin
Jaime Fernandez del Rio jaime.f...@gmail.com writes: I am pretty sure that a continuous sequence of curves that converges to a continuous curve, will do so uniformly. I think a typical example of a curve that's continuous but not uniformly continuous is f(t) = sin(1/t), defined when t 0

Re: Measuring Fractal Dimension ?

2009-06-17 Thread Charles Yeomans
On Jun 17, 2009, at 2:04 AM, Paul Rubin wrote: Jaime Fernandez del Rio jaime.f...@gmail.com writes: I am pretty sure that a continuous sequence of curves that converges to a continuous curve, will do so uniformly. I think a typical example of a curve that's continuous but not uniformly

Re: Measuring Fractal Dimension ?

2009-06-17 Thread Mark Dickinson
On Jun 17, 7:04 am, Paul Rubin http://phr...@nospam.invalid wrote: I think a typical example of a curve that's continuous but not uniformly continuous is    f(t) = sin(1/t), defined when t 0 It is continuous at every t0 but wiggles violently as you get closer to t=0.  You wouldn't be able

Re: Measuring Fractal Dimension ?

2009-06-17 Thread Jaime Fernandez del Rio
On Wed, Jun 17, 2009 at 1:52 PM, Mark Dickinsondicki...@gmail.com wrote: Maybe James is thinking of the standard theorem that says that if a sequence of continuous functions on an interval converges uniformly then its limit is continuous? Jaime was simply plain wrong... The example that

Re: Measuring Fractal Dimension ?

2009-06-17 Thread Mark Dickinson
On Jun 17, 1:26 pm, Jaime Fernandez del Rio jaime.f...@gmail.com wrote: On Wed, Jun 17, 2009 at 1:52 PM, Mark Dickinsondicki...@gmail.com wrote: Maybe James is thinking of the standard theorem that says that if a sequence of continuous functions on an interval converges uniformly then its

Re: Measuring Fractal Dimension ?

2009-06-17 Thread Mark Dickinson
On Jun 17, 2:18 pm, pdpi pdpinhe...@gmail.com wrote: On Jun 17, 1:26 pm, Jaime Fernandez del Rio jaime.f...@gmail.com wrote: P.S. The snowflake curve, on the other hand, is uniformly continuous, right? The definition of uniform continuity is that, for any epsilon 0, there is a delta 0

Re: Measuring Fractal Dimension ?

2009-06-17 Thread Mark Dickinson
On Jun 17, 3:46 pm, Paul Rubin http://phr...@nospam.invalid wrote: Mark Dickinson dicki...@gmail.com writes: It looks as though you're treating (a portion of?) the Koch curve as the graph of a function f from R - R and claiming that f is uniformly continuous.  But the Koch curve isn't such

Re: Measuring Fractal Dimension ?

2009-06-17 Thread pdpi
On Jun 17, 4:18 pm, Mark Dickinson dicki...@gmail.com wrote: On Jun 17, 3:46 pm, Paul Rubin http://phr...@nospam.invalid wrote: Mark Dickinson dicki...@gmail.com writes: It looks as though you're treating (a portion of?) the Koch curve as the graph of a function f from R - R and claiming

Re: Measuring Fractal Dimension ?

2009-06-16 Thread Paul Rubin
Lawrence D'Oliveiro l...@geek-central.gen.new_zealand writes: I don't think any countable set, even a countably-infinite set, can have a fractal dimension. It's got to be uncountably infinite, and therefore uncomputable. I think the idea is you assume uniform continuity of the set

Re: Measuring Fractal Dimension ?

2009-06-16 Thread David C . Ullrich
On 15 Jun 2009 04:55:03 GMT, Steven D'Aprano ste...@remove.this.cybersource.com.au wrote: On Sun, 14 Jun 2009 14:29:04 -0700, Kay Schluehr wrote: On 14 Jun., 16:00, Steven D'Aprano st...@removethis.cybersource.com.au wrote: Incorrect. Koch's snowflake, for example, has a fractal dimension

Re: Measuring Fractal Dimension ?

2009-06-16 Thread Lawrence D'Oliveiro
In message 7x63ew3uo9@ruckus.brouhaha.com, wrote: Lawrence D'Oliveiro l...@geek-central.gen.new_zealand writes: I don't think any countable set, even a countably-infinite set, can have a fractal dimension. It's got to be uncountably infinite, and therefore uncomputable. I think

Re: Measuring Fractal Dimension ?

2009-06-16 Thread Jaime Fernandez del Rio
On Wed, Jun 17, 2009 at 4:50 AM, Lawrence D'Oliveirol...@geek-central.gen.new_zealand wrote: In message 7x63ew3uo9@ruckus.brouhaha.com,  wrote: Lawrence D'Oliveiro l...@geek-central.gen.new_zealand writes: I don't think any countable set, even a countably-infinite set, can have a fractal

Re: Measuring Fractal Dimension ?

2009-06-15 Thread pdpi
On Jun 15, 5:55 am, Steven D'Aprano ste...@remove.this.cybersource.com.au wrote: On Sun, 14 Jun 2009 14:29:04 -0700, Kay Schluehr wrote: On 14 Jun., 16:00, Steven D'Aprano st...@removethis.cybersource.com.au wrote: Incorrect. Koch's snowflake, for example, has a fractal dimension of log

Re: Measuring Fractal Dimension ?

2009-06-14 Thread Lawrence D'Oliveiro
In message slrnh33j2b.4bu.pe...@box8.pjb.com.au, Peter Billam wrote: Are there any modules, packages, whatever, that will measure the fractal dimensions of a dataset, e.g. a time-series ? I don't think any countable set, even a countably-infinite set, can have a fractal dimension. It's got

Re: Measuring Fractal Dimension ?

2009-06-14 Thread Arnaud Delobelle
Lawrence D'Oliveiro l...@geek-central.gen.new_zealand writes: In message slrnh33j2b.4bu.pe...@box8.pjb.com.au, Peter Billam wrote: Are there any modules, packages, whatever, that will measure the fractal dimensions of a dataset, e.g. a time-series ? I don't think any countable set, even

Re: Measuring Fractal Dimension ?

2009-06-14 Thread Paul Rubin
Arnaud Delobelle arno...@googlemail.com writes: I think there are attempts to estimate the fractal dimension of a set using a finite sample from this set. But I can't remember where I got this thought from! There are image data compression schemes that work like that, trying to detect self

Re: Measuring Fractal Dimension ?

2009-06-14 Thread Steven D'Aprano
Lawrence D'Oliveiro wrote: In message slrnh33j2b.4bu.pe...@box8.pjb.com.au, Peter Billam wrote: Are there any modules, packages, whatever, that will measure the fractal dimensions of a dataset, e.g. a time-series ? I don't think any countable set, even a countably-infinite set, can have

Re: Measuring Fractal Dimension ?

2009-06-14 Thread Peter Billam
In message slrnh33j2b.4bu.pe...@box8.pjb.com.au, Peter Billam wrote: Are there any modules, packages, whatever, that will measure the fractal dimensions of a dataset, e.g. a time-series ? Lawrence D'Oliveiro wrote: I don't think any countable set, even a countably-infinite set, can have

Re: Measuring Fractal Dimension ?

2009-06-14 Thread Steven D'Aprano
On Sun, 14 Jun 2009 14:29:04 -0700, Kay Schluehr wrote: On 14 Jun., 16:00, Steven D'Aprano st...@removethis.cybersource.com.au wrote: Incorrect. Koch's snowflake, for example, has a fractal dimension of log 4/log 3 ≈ 1.26, a finite area of 8/5 times that of the initial triangle

Measuring Fractal Dimension ?

2009-06-12 Thread Peter Billam
Greetings. Are there any modules, packages, whatever, that will measure the fractal dimensions of a dataset, e.g. a time-series ? Like the Correlation Dimension, the Information Dimension, etc... Peter -- Peter Billam www.pjb.com.auwww.pjb.com.au/comp/contact.html -- http

Fractal curve

2005-11-27 Thread Steve Heyburn
Hello there, I am studying programming at University and we are basing the course on Python. We are currently looking at fractal curves and I was wondering if you could email me code for a dragon curve please, or a similar fractal curve. Thank you Steve -- http://mail.python.org/mailman

Re: Fractal curve

2005-11-27 Thread Steve Holden
Steve Heyburn wrote: Hello there, I am studying programming at University and we are basing the course on Python. We are currently looking at fractal curves and I was wondering if you could email me code for a dragon curve please, or a similar fractal curve. http://www.google.com