Talk:Buddhabrot

Reference to Buddha

I'm pretty sure this is named after "Laughing Buddha"/Budai depictions, and not after Buddha. Buddha is traditionally described as very skinny, which doesn't really match these images. Khim1 (talk) 09:59, 5 July 2020 (UTC)

Orientation

Why do the image captions explicitly state everywhere, whether a picture is rotated or not? The axes can be chosen arbitrarily anyway; the choice of the axes does not make one picture more correct or more original than any other. Or is it really stated anywhere, that the real axis should be horizontal and the imaginary one vertical?? I doubt it. — Pt _(T) 21:58, 20 Apr 2005 (UTC)

The convention in mathematics is always to have the real axis horizontal and the imaginary one vertical. You are right that it is arbitrary, but it is a pretty strong convention.

Maybe put up an image of the "certain depictions of the Buddha" for comparison? Subjectruin 10:40, 3 April 2006 (UTC)

picture of it upside down

add a picture of it upside down pleaseOxinabox1 11:49, 15 August 2006 (UTC)

Butterbrot?

Is it a coincidence, that its name sound like Butterbrot (bread and butter) in German? I hardly could stop laughing. —Preceding unsigned comment added by 82.135.5.192 (talk • contribs) 23:30, 18 December 2005

Hehe, I was just about to post the same comment. :-) —Preceding unsigned comment added by 84.178.158.195 (talk • contribs) 14:09, 23 February 2006

I went ahead and deleted it. --Zifnabxar 03:03, 12 July 2006 (UTC)

I undid it yesterday because I doubt that this similarity is a pure accident. The association whith "butterbrot" springs in your mind immediately if you are a German speaker like me. To us, it's a kind of an embedded mathematical joke.

Fortunately, Green and Gardi are still alive, and so we can ask them whether they knew about the embedded pun when Gardi coined the name and Green adopted it.--Slow Phil (talk) 11:53, 24 January 2013 (UTC)

April Fools?

This article is kind of silly. —Preceding unsigned comment added by 72.19.75.106 (talk • contribs) 05:25, 3 April 2006

How so? All it is is a form of rendering. You also didn't need to make your little "utter crap" comment at the bottom either. —Preceding unsigned comment added by 195.195.168.33 (talk • contribs) 12:26, 3 April 2006

Description needs to be clearer

I used to do a fair bit of fiddling with fractals, and I'm well versed with the rendering method for mandelbrots and julias...but I still don't really get the method for this one. I hate to think how a true layman would cope. Can someone attempt to elaborate a bit on the rendering method, perhaps by turning it into pseudocode or a simple algorithm? Stevage 21:33, 3 April 2006 (UTC)

I may be completely wrong, but I think that what's happening here is something like this: for each value of c you construct a $m\times n$ matrix, each element representing the corresponding pixel in the image. Then for this c, everytime the succession hits a particular pixel, the corresponding element in the matrix is added one unit. In the end, you work with the set of matrices and a color algorithm to produce your coloring. Either way, I'm also very interesting in really understanding what's going on and I certainly think the article needs a clearer text. jοτομικρόν | Talk 23:13, 3 April 2006 (UTC)

All good, except for the "succession hits a particular pixel" and "corresponding element" bits. Can you elaborate? :) Stevage 06:17, 4 April 2006 (UTC)

Again, I emphazise that I may be wrong. The succession (z_n) hits a particular pixel (P) when n is such that the point z_n is "within" that pixel, that is, if you wanted to paint the point z_n on the screen, you would have to paint the pixel P because it is the best approximation to z_n. By corresponding element I mean exactly the same: for each point, there is a matrix whose elements are in one-to-one correspondence to the screen pixels. That said, $m_{i,j}$ corresponds to pixel (i, j). Let's considerer c = 1 and a screen in which each pixel is 1 unit wide:

• z₁ = 1;
• z₂ = 2;
• z₃ = 5;
• ... (it escapes to infinity).

So for this point's matrix, the element that correspond to the pixel that contains the point 1 + 0i (pixel (1, 0)) is incremented, as are those elements corresponding to the values 2 + 0i (2, 0), 5 + 0i (5, 0), etc. jοτομικρόν | Talk 17:44, 4 April 2006 (UTC)

I understand what you are describing but do not understand how these matrices (one for each pixel) relate to the final render. Can someone explain?69.121.103.100 06:11, 10 April 2006 (UTC)

The colour is based on the number of times a value z has "passed through" the pixel... more times is brighter. I'm not a mathematician myself, so it's hard for even me to explain... Evercat 23:25, 14 April 2006 (UTC)

It basically shows the path each initial value traces out over many iterations. pixels become brighter as more of those paths go trough them.82.176.178.244 (talk) 15:32, 15 June 2011 (UTC)

Discovery

Does the phrase "Melinda Green (then Daniel Green)" refer to a single person? It's not clear from the wording at the moment.   — Lee J Haywood 23:04, 5 January 2007 (UTC)

I'm interested as well.Javaisfun 04:38, 7 February 2007 (UTC)

It is a single person. Daniel Green underwent a sex change and now goes by Melinda Green. (See this usenet post.) I have clarified this in the article. --Rayno 05:56, 5 June 2007 (UTC)

I have removed the reference and explanation regarding Daniel in the article, but I am leaving it here for some measure of fairness, since it is "public knowledge". It is bad form to refer to someone as "Jill (used to be Jack)" especially if it adds nothing to the discourse and leaving it out would remove nothing. Lets be good sports about this. --Lionelbrits 00:48, 4 August 2007 (UTC)

I disagree. Melinda Green did not do what is claimed here, since she was not Melinda Green. The situation is no different than a reference to activities of a now-married woman before her name was changed. —Preceding unsigned comment added by 207.140.171.5 (talk) 4 August 2007

The problem is that the usenet post I cited gives the name Daniel Green, so without some explanation it makes no sense. Evercat 00:59, 16 September 2007 (UTC)

Buddha?

To me it looks more like the head of a tiger, or a fox. —Preceding unsigned comment added by Dehagido (talk • contribs) 09:43, 23 September 2007 (UTC)

Confusing

Previous researchers had come very close to finding the precise Buddhabrot technique. In 1988 Linas Vepstas relayed images of the Buddhabrot to Cliff Pickover for inclusion in Pickover's forthcoming book Computers, Pattern, Chaos, and Beauty. This led directly to the discovery of Pickover stalks. These researchers did not filter out non-escaping trajectories required to produce the ghostly forms typically reminiscent of Hindu art. Green first named it Ganesh, since an Indian co-worker "instantly recognized it as the god 'Ganesha' which is the one with the head of an elephant." The name Buddhabrot was coined later by Lori Gardi.

This is confusing. It makes it sound like they were looking for the Buddhabrot technique. I presume they were just trying things and they came close to producing the Buddhabrot but didn't. Also, it seems to suggest they sent Buddhabrot images even though it also implies that these aren't actually Buddhabrot images since it says Daniel/Melinda Green invented it and that they only came close i.e. it contradicts itself. Nil Einne 12:16, 8 October 2007 (UTC)

Nil Einne is correct that that wording was confusing. I changed "images of the Buddhabrot" to be "similar images". There might be better descriptions but this resolves the contradiction. Melinda Green 26 April 2009 —Preceding unsigned comment added by 70.231.155.213 (talk) 20:14, 26 April 2009 (UTC)

Rendering

Hi there, with a new account, I still cannot upload images. I'd like to extend the text with the following interpretation:

The Buddahbrot can be seen as an overlay convergence-image of maps of the complex plane onto itself under different powers of the Mandel iteration z^2+c. Therefore, a natural way of coloring is to use a color map of the complex plane, then do successive iterations and pile color information in the overlay image. Through this You can track to some extent, which points from the original complex plane result in which structures in the buddhabrot fractal. In order to obtain a good image, one uses minuite random fluctuations in the starting point positions so that several passes enable to generate a stable image. Using this technique with all points, here's a first result: (have a look at wkw gruppe fraktale). Wikistallion (talk) 09:23, 4 August 2009 (UTC)

I don't think that these alternative rendering variations and the further additions that Wikistallion followed-up with belong here because if they did, then there are all sorts of other variations that would then also seem to belong as well. At best, I think the idea of moving the pixels of an image under the control of a fractal function deserves it's own parallel page. Also, the suggestion of randomizing initial points taken from a grid is not really an improvement over sampling completely random points. My inclination is to simply remove this section as not really adding much to the particular topic but I thought I'd best declare my intent here to give others a chance to weigh in first. If nobody says anything in a month or two then I'll do that. Cutelyaware (talk) 06:19, 14 October 2009 (UTC)

After waiting 8 months without objection, I removed the Renderings section as planned. I also removed redundant images and the text describing impressions of similarity to faces and viscosity. Cutelyaware (talk) 20:08, 28 June 2010 (UTC)

Rendering complexity

Because rendering Buddhabrot involves potentially iterating twice over each sample (once to test if it escapes, and again to plot its path if it does), it is more computationally intensive than standard Mandelbrot rendering techniques.

This is not exactly true. Since the first iteration, which is used to check whether the sample escapes or not, yields the exact same results as the second iteration, which is used to plot its path, one could just buffer the series of Z during the first iteration and use the buffer to plot the path if the sample escapes. I'm using this in my application and it works just fine - no need to do the same work twice. —Preceding unsigned comment added by 83.228.170.68 (talk) 17:37, 5 August 2010 (UTC)

Buddhabrot (red-rotated)

Another rendering of the Buddhabrot is at http://en.wikipedia.org/wiki/File:Buddhabrot-red-rotated.png —Preceding unsigned comment added by 208.40.206.69 (talk) 12:31, 28 August 2009 (UTC)

Page move/renaming

Quit surprised by the move/renaming of the page. Of the three references two refer to it as Buddhabrot and the first is its initial announcement before it had been given a name. The other external links also confirm that Buddhabrot is the generally accepted name.--Salix (talk): 14:38, 31 August 2010 (UTC)

iterations back the front

I really like the images of the BB with different numbers of iterations. I'm a non-techie,but everywhere else, such progressions are depicted in ascending order, with the first image showing the lowest number of iterations, and succeeding images showing the emerging Set as the iterations become more numerous.

I can't see why this is reversed here. It's like showing depictions of the development of human being, STARTING with a man, and then with later pictures ending up showing him as a new-born. Once again, I'm a non-techie, but this one puzzles me. Myles325a (talk) 10:26, 18 February 2011 (UTC)

• Thanks for bringing this up. I can't see why it's back to front either so I reversed it. Now it's in the order 20, 100, 1000, 20000, 1000000. Purpy Pupple (talk) 20:14, 18 February 2011 (UTC)

Reversed addition regarding filtering & interesting trajectories

I removed an addition from Kri that I feel the need to explain why. He said

"Yet another technique many have observed leading to a more interesting image is to plot only the paths for points c which escape but do not escape until some minimum number of iterations (for example 1,000 or 1,000,000), although no good name has been given this variant of the Buddhabrot. When the number of iteration it takes for a point c to escape becomes very large, it can also be interesting to isolate it and look at the trajectory of that point alone since it can generate some interesting shapes."

He makes two points here. The first regards filtering out portions of the trajectory data. From my direct experience it initially seems like a good idea to filter out what appears to be data that is redundant to more than one color channel. The problem is that doing so does not add anything to the resulting images other than some "edge effects" at the chosen "settling-in" thresholds. These edge effects are not part of the underlying mathematical object any more than are artifacts created by sampling from too small of a spatial domain.

His second point is regarding the interesting trajectories that some initial points generate. It is true that some trajectories are fascinating to observe in isolation, however this has nothing to do with the Buddhabrot technique any more than it does for the Mandelbrot set. Cutelyaware (talk) 03:38, 18 July 2011 (UTC)

I don't think that it is a problem that nothing is added to the resulting image. The edge effects are the whole point of using this rendering technique, so they are definitely not artifacts (I suppose you took a look at the link in the reference). I think the rendering technique is a nuance of the Buddhabrot (at least as much as the Nebulabrot is) and that it therefore makes sense to have it there, and that it is an interesting addition to the article. If you still want it removed, you can perhaps see if you can find a Wikipedia clause that forbids it being there, since we don't seem to agree on this point. However, in the mean time, I will bring it back again. I can maybe agree with what you say about the second point so therefore I won't bring that back. —Kri (talk) 12:49, 18 July 2011 (UTC)

Kri: I'm glad that you looked to the discussion page before reversing my removal of your text. The main problem I have with it is that you are simply saying "here is another tweak that generates interesting results". First, it is completely subjective to call it "interesting" and you do not say why it is interesting. Second, there any number of other tweaks that some people will find interesting but that doesn't make them pertinent either. You are right that the nebulabrot is also a kind of tweak with subjective results. The thing that I believe makes the nebulabrot and Buddhagram variations pertinent to the Buddhabrot is that I am the inventor of all of these techniques and I feel that gives me a bit more license to decide what is relevant. I doubt there is any "Wikipedia clause" forbidding your additions but I may ask an official for a ruling on this point. I am glad that you are looking for interesting extensions to my methods and I encourage you to publish them independently, but please not on the Buddhabrot page. Cutelyaware (talk) 05:43, 25 July 2011 (UTC)

The reason I think it's interesting is simply because I think it looks interesting and not because it's especially interesting from a mathematical point of view. I think the fact that there is a section in the article called Nuances kind of invites people to add tweaks, and I guess I was surprised and didn't really understand why my addition of a tweak was removed from the article.

If you say there are many other tweaks that people will find interesting and you want to keep the article as 'clean' as possible, I understand and respect that. In that case we should make it clear what kind of nuances that are acceptable and why for example the Nebulabrot qualifies and some other methods don't. —Kri (talk) 12:06, 26 July 2011 (UTC)

References

Looks like Cartman

It looks like Cartman wearing a tuque with a pompom on top.Doubledork (talk) 00:41, 26 January 2012 (UTC)

Notability

Could someone explain the notability of this article via WP:Notability? It is pretty clear that the object is not notable from the point of view of Mathematics, so how does this notability arise? The article currently gives the impression that this is simply an object that was generated by hobbyists playing around with algorithms for generating the Mandelbrot set, and that they found aesthetically pleasing.

There is, of course, nothing wrong with that, and this doesn't exclude notability. The question is, what distinguishes the object from hundreds of other objects that have likely been discovered in a similar way? Are there secondary articles discussing it, or has it been influential in e.g. creating mathematical artworks? Are there serious secondary sources treating it? Is the notability established in some other way? This doesn't seem apparent from the article or its sources. L. R-G (talk) 21:40, 25 February 2013 (UTC)

This is notable, as the single secondary source proved. How do you get to decide what is an "obscure" journal and what is not? Does it need to be published in Nature before it meets your threshold? There are currently 29 results under Google scholar for "buddhabrot," most all of them are secondary sources that meet Wikipedia's notability guideline. What is your issue exactly? Please find one from the following list that meets your criteria, add it as a reference, and remove the unnecessary notability tag. http://scholar.google.com/scholar?hl=en&q=buddhabrot&btnG=&as_sdt=1%2C5&as_sdtp= Lgstarn (talk) 21:29, 29 March 2013 (UTC)

Please read WP:Notability "availability of secondary sources covering the subject is a good test for notability." Notable. QED. Lgstarn (talk) 21:33, 29 March 2013 (UTC)

Also pretty interesting how you decided it was "clear that the object is not notable from the point of view of mathematics" when people are publishing articles about the Buddhabrot in journals such as "International Journal of Bifurcation and Chaos in Applied Sciences and Engineering." http://www.worldscientific.com/doi/abs/10.1142/S0218127413500156 It is not easy to decide what would and would not be interesting or notable to mathematics. 137.78.253.128 (talk) 22:55, 29 March 2013 (UTC)

Sorry if this comes across as an ad hominem attack, but looking at your talk page it becomes clear what the real issue is - you are a "professional" mathematician, and this was discovered by "hobbyists." In other words, it's the not invented here syndrome. 137.78.253.128 (talk) 22:58, 29 March 2013 (UTC)

I do not understand the hostility. I have not suggested the article for deletion or anything of the kind. I simply felt - and still feel - that the notability has not been established. I read the notability guidelines before I tagged the article, and I have seen nothing in there that suggests that being referenced in some published work is sufficient to establish notability - instead, one should weigh the reliability of sources etc. There are many other interesting topics that I don't feel would meet the notability guidelines - I would class most of my own theorems and definitions within this category, although I could likewise cite 'secondary sources' that mention them.

I thought it would be possible to have a factual discussion about the topic here, but it feels almost as though some people are somehow personally invested in the topic. I am indeed a professional mathematician, but I don't see how that is relevant. I can speak to the fact that this object is not notable within mathematics - in fact, I am not sure that there is a precise mathematical object that is being represented by the image, given that the image depends on various parameters that can be chosen in a non-canonical way.

However, the image is definitely beautiful, and it was inspired by mathematics, which is great. My question was, and still is, what the evidence for its notability is. This is not clear from the article. I normally would expect, for a notable subject, a number of references in highly ranked international publications (and no, it doesn't have to be 'Nature') and/or with a significant number of citations; or perhaps some significant coverage in national/international media etc. In my view the citations currently given are a little bit dubious - at least one of them itself refers back to Wikipedia, which suggests some issues.

I'm not interested in killing this article, or to pick a fight. I'm simply asking for someone to explain to me (and other potential readers) what the notability of the subject is. If a sensible discussion cannot be had, and you resort to ad hominem responses rather than discussing the subject, then I'm perfectly happy to go away. L. R-G (talk) 00:45, 30 March 2013 (UTC)

Following through from the google scholar search[1]. None of the papers listed have many citations themselves, the maximum seems to be three. The first paper "What is the Relatedness of Mathematics and Art and why we should care?" gives a clue to its importance: more as a visual image and less as a piece of mathematics with wider reference. (Also note the circular reference to this page in the paper) Those papers also seem to generalise the method, the hit counting aspect of the methods is perhaps its biggest contribution.--Salix (talk): 08:47, 30 March 2013 (UTC)

The hostility probably comes from you being perceived as trying to act as a gatekeeper of the notability of all things mathematical like the Mathematical Master from Oscar Wilde's Little Prince, which is quite an unhelpful attitude to take, but let's set that aside and discuss things factually. Your argument that it is not notable in mathematics ignores the fact that it is, in fact, noted in several secondary sources by people who would probably call themselves mathematicians. It is receiving new and additional attention as evidenced by the 2012 and 2013 research, making it notable, by definition. And yes, perhaps some of the sources in the Google scholar search are not reliable - no surprise there, but let's not straw man. Also, on WP:Notability I don't see anything about the number of citations necessary to establish notability, just that there is editorial review (which is the case for any peer-reviewed journal). Regarding international media coverage, while I see a reference to this fractal in Tricycle Volume 15 Issue 3-4 (the most popular Buddhist periodical publication), this fractal is clearly less notable than, say, the Mandelbrot or Julia fractal. However, just because there are "non-canonical parameters" (which ones, by the way?) does not mean anything; the Julia set has "non-canonical" parameters that vary the fractal, as does the Buddhabrot. I agree with Salix, the notability here from the mathematics side includes a clever way of boxing the parameters and visualizing the Mandelbrot set; it is actually another quite "canonical" view of the Mandelbrot set. That aside, in my opinion the notability could be established purely from the perspective of this being a piece of mathematical art ( see e.g. http://books.google.com/books?id=fv3sltQBS54C&lpg=PA108&dq=buddhabrot&pg=PA108#v=onepage&q=buddhabrot&f=false http://books.google.com/books?id=SJRNoOaXs2wC&lpg=PA76&dq=buddhabrot&pg=PA76#v=onepage&q=buddhabrot&f=false). Lgstarn (talk) 19:03, 1 April 2013 (UTC)

Also I would recommend reading WP:WHYN. Lgstarn (talk) 19:07, 1 April 2013 (UTC)

I would appreciate a less condescending tone. I read WP:WHYN well before raising the issue, and in turn would ask that you read WP:AGF, and read what I actually wrote rather pre-judging my motives. Far from "trying to act as a gatekeeper of the notability of all things mathematical", my point was and is that there are many interesting mathematical results and topics that I feel would be notable under Wikipedia's policy. I realize that application of this policy is rarely black-and-white, and different editors can take a more or less inclusive point of view. Being 'noted in several secondary sources by people who would probably call themselves mathematicians' is too weak a justification, because it applies to almost anything ever dreamed up in mathematics (even things that are not considered notably even within mathematics, or have turned out to be totally wrong).

The reason why I referred you to WP:WHYN is that notability is used to make sure 'that we're not passing along random gossip, perpetuating hoaxes, or posting indiscriminate collections of information.' This article is none of those. In addition, being noted in several secondary sources is quoted as "the" test for notability. Notability is not decided by anything other than having reliable sources that cover the topic. If you have things that are dreamed up by mathematicians, have significant coverage, and have reliable sources, they do in fact warrant an article as per Wikipedia policy WP:GNG. Lgstarn (talk) 05:23, 2 April 2013 (UTC)

Clearly we disagree on what constitutes 'significant coverage' and 'reliable sources'. Which is fine, the policy was never intended to be absolute, but to be implemented through discussions such as this one. L. R-G (talk) 10:05, 2 April 2013 (UTC)

To clarify my comment on parameters, the Mandelbrot set, and the Julia set of a polynomial (or rational function) are mathematically defined sets in the complex plane. They do *not* have 'non-canonical parameters', contrary to what you stated. The image that you get from the method described in the article depends on the resolution you use for your pixel, and how many iterations are computed. For pictures of the Mandelbrot set and Julia sets, there is a limit object that these images are approximating. It is not clear that there is any such corresponding object for the 'Buddhabrot'. There is currently no mathematical theory of the Buddhabrot (including in the articles that have been referenced by you). If you search on mathscinet ('Mathematical Reviews' on the net) for 'buddhabrot', there are no results. Taking everything together, there is conclusive evidence that the 'Buddhabrot' is not a notable object in mathematics at the present time.

The Buddhabrot set *is* a mathematically defined set in the complex plane just like the Mandelbrot and Julia sets. The mathematical definition of this set is: let C be an approximation of the converse of the Mandelbrot set, and define a grid spacing (delta x, delta y) and a number of iterations m. Let F(C,i,j) be the number of times the grid box (i,j) is visited as the set C is iterated through the Mandelbrot iteration m times. Let G(C,i,j) = F(C,i,j)/max_(i,j) F(C,i,j) for all i and j. Now define the set B to be the limit of G(C) as C goes to converse of the Mandelbrot set, delta x and delta y goes to 0, and m goes to infinity. The Buddhabrot set is the set of all non-zero elements within B. So there's your mathematical definition of the set right there. An image is an image, and should not be confused in any way with the underlying set. A Mandelbrot or Julia set image also depends upon the resolution you use for your pixel and how many iterations are computed. Furthermore, your statement about the mathematical theory of the Buddhabrot being lacking and the search on mathscinet coming up empty is nothing more than a lack of evidence of notability, certainly not the evidence of a lack. Lgstarn (talk) 05:23, 2 April 2013 (UTC)

There is no reason for the limit as you define it to exist (i.e., be independent of the way that you let your parameters tend to 0 respectively infinity). Indeed, as you have written it (without requiring any particular properties of the 'approximation', it almost certainly does not exist. For the set called the 'Anti-Buddhabrot' in the article, it is somewhat easier to imagine what the object might be: presumably an average of all the possible physical measures for the maps in the (interior of) the Mandelbrot set. Again, it is far from clear that this gives something non-singular. There are lots of other points here, but we are not trying to do original research on the 'Buddhabrot'. If you have a reference that seriously discusses a mathematical object that the 'Buddhabrot' is approximating, then feel free to post it, and I will take a look at it. L. R-G (talk) 10:05, 2 April 2013 (UTC)

This is an interesting conversation that would be lovely to have in person over a cup of caffeinated beverage with a pen and napkin. I'm not sure why you said the limit doesn't exist depending on how you choose the set (I was thinking you simply take a random sampling of points within c < 2 that converges in the limit to the converse of the Mandelbrot within this ring), and would very much like to hear your reasoning behind why this limit does not exist before I try to prove why it does exist. I would think that the limit not existing would be a far more interesting result than it actually existing. This is original research, but hey, this is a talk page. Lgstarn (talk) 21:48, 2 April 2013 (UTC)

The Buddhabrot is not a set or any other particular mathematical object. It is a rendering/visualization technique that can be applied to any escape-time fractal, not just the Mandelbrot set. Given a set of rendering parameters, the images develop much like a photographic image, and appear to converge on a final image, though I doubt that has been proven. The images are density maps of where trajectories prefer to spend their time before escaping. It is notable for 1) being an alternative rendering method as valid as the one normally associated with the Mandelbrot set, 2) for its beauty and surprising similarity to Hindu religious art, and 3) for the interest it generates in both computer science and spiritual communities. Cutelyaware (talk) 22:44, 29 June 2015 (UTC)

That being said, I entirely agree that a more likely avenue to establishing notability is as a piece of mathematical art. The citations from books that you list are promising - I still think they are a little bit on the thin side, and it would be good to have some stronger evidence, but it is a start. I think it would be good to include these sources in the article, and to clarify the role that the Buddhabrot has as mathematical art.

Well, I suppose then we can agree on something. This is notable from several angles, and would appreciate it if you would add in the art references you find appropriate. If not, I can do it as well. Lgstarn (talk) 05:23, 2 April 2013 (UTC)

A next issue to consider (as a separate topic from notability) is that much of the article looks like original research; at least it does not seem clear that this material has references in the secondary sources listed in the article. The section about the similarity between the name and the word 'Butterbrot' looks particularly out of place, but the discussion regarding the logistic family also is rather unclear. I'm happy to have a go at revising the article sometime in the near future, but my feeling is that I would remove more than some editors would be happy with ... L. R-G (talk) 21:41, 1 April 2013 (UTC)

Fairly little of the article is original research, it just seems to me you have just not read the references in sufficient detail. The Butterbrot section has already been removed. By all means feel free to have a go at revising the article. Be bold! Likewise I will also be bold in making sure you do not remove anything that is not original research. Lgstarn (talk) 05:23, 2 April 2013 (UTC)

• I do agree that the notability seems more in the area of mathematical art than mathematics itself. A Google search reveals 142,000 results, of which most are hobbyist websites. Feel free to be bold and "have a go at revising the article". I am always appreciative when an expert tries to improve Wikipedia articles. By the way, the stuff about 'Butterbrot' was recently removed by Salix alba.

As a minor point, maybe someone from WikiProject Systems should clarify why this article deserves "Mid-Importance" rating and perhaps reëvaluate it.

As an even more minor point, Oscar Wilde wrote The Happy Prince and not The Little Prince. dllu (t,c) 05:05, 2 April 2013 (UTC)

I would also recommend that you do not overly attach importance to a single self-professed expert - Lasserempe is not the only professional mathematician who is published in this thread. Lgstarn (talk) 05:31, 2 April 2013 (UTC)

Here is a summary of my arguments: there is significant coverage of the topic of this article from several angles: a) from the mathematics side, it is mentioned in no less than three secondary source articles in peer reviewed journals; b) from the mathematical art side, there is also significant coverage. This article is notable no matter how you look at it. The Buddhabrot set is in fact another way of visualizing the Mandelbrot set that is as canonical as one could ask for. In fact, this article could be merged into the Mandelbrot fractal page, but this would likely lead to confusion, and since there is significant coverage of this method on its own, and we all agree it is at least notable as mathematical art, I recommend we keep the article as is without any notability tag. Let's instead direct our efforts to improving the page itself (and possibly improving the mathematical theory in our own private lives). Lgstarn (talk) 06:33, 2 April 2013 (UTC)

• I understand that you too are also an expert in a relevant field (PhD of Computer Science) and also welcome your input! So too is Salix alba an expert in mathematics. In fact, I seem to be the only person who is not and expert here. I do think this article is quite notable (just that it seems to me more notable in mathematical art than mathematics). I agree that our efforts should be directed to improving the page itself. Personally, I would be fine if it were merged into the Mandelbrot set article although the said article may get too long. I would prefer that the article stays, though, and agree with Lgstarn's recommendation that it stay here without the notability tag. dllu (t,c) 06:39, 2 April 2013 (UTC)

I think merging into Mandelbrot set is a bad idea. MS is a very important topic which has formed a cornerstone of a whole field of mathematics. Buddhabrot is an interesting aside and a merge would give it WP:UNDUE weight.--Salix (talk): 07:21, 2 April 2013 (UTC)

Nuances - Section

The five images that depict the Buddhabrot with increasing iterations don't open properly. A white image is all that is displayed when I click for a larger version. Would it be inappropriate for me to replace them with my own, non-white versions? I'd put up equivalent images with the same iterations and all. Or is there a way to restore the originals back? Lucky Potatoe (talk) 06:24, 25 August 2013 (UTC)

• The reason why they appear white is that the pictures are white against a transparent background. Most web browsers have a white background so it ends up being white against white. If you view them against a black background instead it will be perfectly clear. I can change the transparent background to a black background if needed. dllu (t,c) 21:52, 25 August 2013 (UTC)

• There are numerical problems (viz. floating point rounding errors) in the pic with 100,000 iteration, which lead to its apparent lack of symmetry. — Preceding unsigned comment added by ChronotopicXeal (talk • contribs) 09:31, 1 February 2019 (UTC)

External links

@Cutelyaware: The external links I removed do not comply with WP:External links guidelines. Please indicate here why you think they are " crucial external references". If you want to use them as references then they should be moved to the reference section. Sarahj2107 (talk) 12:07, 8 January 2016 (UTC)

The first link is the closest thing to an official page though I now see that it's already referenced. The second can probably be turned into a reference for the mention of Linas Vepstas though I'm not 100% certain the linked images are the ones being referenced. The links that you had retained seem to be simply good examples of the great many excellent implementations, modifications, renderings, and descriptions of the technique. I don't know the policy on that matter and so will differ to your judgement on that but would like to get your reasoning and guidance on how best to deal with such additions as that has been a problem in the past. Cutelyaware (talk) 12:28, 8 January 2016 (UTC)

I will explain my reasoning for removing each link.

• Buddhabrot discoverer Melinda Green's page - already a ref, as you stated.
• Buddhabrot discoverer Linas Vepstas page -doesn't comply with WP:ELNO point #1 - "Any site that does not provide a unique resource beyond what the article would contain if it became a featured article." It also doesn't appear to be an page for the discoverer as claimed (and such page would need to be official). but could be used as a ref.
• Buddhabrot page in the Mu-Ency Mandelbrot Set Encyclopedia - also doesn't comply with WP:ELNO point #1. Could also probably be used as a ref if nothing better is available.

I left the other two because they are more marginal and I didn't want to remove them all. But after having another look, I think Buddhabrot page from the Gallery of Computation can be removed as it doesn't comply with WP:ELNO point #1 and there are images available on Commons which is linked. I will leave the last one as it contains a link to other articles on the subject and may have more detail than would ever be in the Wikipedia article.

I am currently going through a huge backlog of pages tagged as needing external link cleanup, the oldest of which includes this page dated to August 2010. So these pages have been linked as having problems for a really long time and I feel that someone needs to just go in and be merciless in terms of what is removed. The relevant policy which should also be considered is WP:LINKFARM which states that Wikipedia is not a repository for links. Feel free to use the removed links as references if possible and let me know if you want any more clarification. Sarahj2107 (talk) 13:21, 8 January 2016 (UTC)

I turned the Vepstas link into a reference (please review) because it contains historically valuable images. That alone suggests to me that it does not violate WP:ELNO but perhaps the reference is better.

One thing you could help with is advising what to do with people showcasing their variations on the technique. The first reference by Jovanovich is such an example. It deserves recognition because it brings much more than the usual sort but this page shouldn't turn into a link farm for every "me too" site. My suggestion to him when removing it previously was to create a "Buddhabrot Variations" page where everyone can link to their implementations pages and to add his there. Complicating this is the fact that some variations seem natural (such as described in the Nuances section) and seem to belong here, and others do not, and often the difference seems to be in the obviously subjective beauty of the results. The problem is not as bad as it once was but I'm never sure how to approach it, perhaps because I still don't understand much of the information on external links. Cutelyaware (talk) 00:14, 9 January 2016 (UTC)

1,000,000 Iterations Image

In the section "Nuances" there is an image of the Buddhabrot with 1Million iterations. It is asymetrical around the Real Number Line which the actual Buddhabrot is of course not. I understand, this article concentrates also on the aesthetic aspects of the subject and I would dislike seeing the image removed but maybe a comment would be needed. I myself, when I saw the Image a few years ago and quite new at University have taken from this (impressive) image a misconception of the structure in complex numbers away. I am not that sure what to change in the article. || JulSwrd (talk) 20:48, 19 April 2020 (UTC) ||

It's not exactly wrong. Ideally you would continue the process until the image was completely converged, but at very high iterations, it could take prohibitively long to get a converged result. And the structure that gets generated along the way (what you see here) is quite interesting in its own right because it does let you see some of the behavior of those complex trajectories. The asymmetry is because the programmer didn't mirror all the plotted points as a timesaving device. There's a fair amount of room here for creative expression while staying true to the technique. It's just helpful to understand what you're looking at. Cutelyaware (talk) 09:21, 20 April 2020 (UTC)

If you read the section on how it's done, there this sentence: "Next, a random sampling of {\displaystyle c}c points are iterated through the Mandelbrot function.". Since it's a random sampling of points, you may end up with a different set of points on either side of the image. This is normal. Of course, the more points you start with, the more even and detailed it would look. I would like to regenerate these images with vastly more points. I think that with modern computers it should be possible to generate much better Buddhabrots than the images from 2008. dllu (t,c) 09:51, 20 April 2020 (UTC)

You're certainly welcome to generate better images, though if you sample enough points to get a fully converged image, then you can get the same result in half the time by mirroring the points as you plot them. In other words, not doing that mirroring only makes sense if you're not going to take it all the way to convergence. Cutelyaware (talk) 09:58, 20 April 2020 (UTC)

Thank you very much for clarifying. I might actually do some renderings to convergence in the future. ||JulSwrd (talk) 12:41, 20 April 2020 (UTC)||

No problem. Just be sure to permanently save your array of exit values, because you'll probably want to experiment with how to turn those into intensity (pixel) values. A linear ramp produces poor results. Histogram equalization seems to be a natural approach.Cutelyaware (talk) 23:05, 20 April 2020 (UTC)

New Open Source Buddhabrot generator

I've just written a fairly fast program to generate high resolution Buddhabrots. GitHub link. And here is an example 16384 × 16384 file with 2000 iterations: (LARGE 96 MB FILE) dllu (t,c) 05:00, 21 April 2020 (UTC)

Extraordinarily high resolution Nebulabrot

I've also just uploaded 16384 × 16384 Nebulabrot. On my 12-core computer this took merely 10 minutes to generate. The parameters were chosen to be the same as File:Nebulabrot (5000, 500, 50).png but my gamma correction etc were different and my number of samples and escape radius may also have been different. dllu (t,c) 07:39, 21 April 2020 (UTC)

Other Powers

multi-Buddhabrot set (Negative and Positive powers)

Multibrot set, Buddhabrot, Anti Buddhabrot at 5000 iterations all the images were generated using the same RGB coloring code

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  Multibrot set, Buddhabrot, Anti Buddhabrot at 5000 iterations

• The Buddhabrot from powers 2 to 8

• The Buddhabrot Conjugate from 2 to 6