From: owner-fractint-digest@lists.xmission.com (fractint-digest) To: fractint-digest@lists.xmission.com Subject: fractint-digest V1 #288 Reply-To: fractint-digest Sender: owner-fractint-digest@lists.xmission.com Errors-To: owner-fractint-digest@lists.xmission.com Precedence: bulk fractint-digest Friday, September 4 1998 Volume 01 : Number 288 ---------------------------------------------------------------------- Date: Wed, 02 Sep 1998 22:14:39 -0600 From: Phil McRevis Subject: (fractint) Re: fractals in postscript wdelange@biochem.nl (Wim de Lange) writes: > Some years ago there was an article in the Byte about postscript. And > in this article there was an postscript program to calculate the > mandelbrot set. Is there someone who has this article and/or the > postscript program for this. I've now an postscript printer > available, and I want to test this on the printer. Its not that hard to do, but there are a couple reasons why you probably don't want to compute M in PS: o M is floating-point intensive and most PS printers aren't optimized for floating-point math. o PS is interpreted and the burden of interpretation only adds to the already heavy computational burden of computing M. o You'll probably get faster results by computing M in GIF format and converting the GIF image to PS and printing the image. However, if you just want to see it run 'for yucks', try the following postscript file on your printer: You may need to tweak the file in an editor to adjust the end-of-line convention (postscript is ASCII and that file has the unix end-of-line convention). - -- http://www.xmission.com/~legalize/ Legalize Adulthood! legalize@xmission.com ``Ain't it funny that they all fire the pistol, - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: 03 Sep 98 07:46:02 GMT From: wdelange@biochem.nl (Wim de Lange) Subject: (fractint) Re: fractals in postscript Op 2 Sep 98 om 22:14 schreef Phil McRevis over: "Re: fractals in postscript" > Its not that hard to do, but there are a couple reasons why you > probably don't want to compute M in PS: I'm well aware of them I played many years with fractals, and wrote little basic programs before I was aware of fractint and such stuff. And long ago I had that article, and I found it 'funny' (not the right word, my english is not good enough) that a printer has a programming language that is capable of calculating the M-set. > andelbrot_color.ps> I downloaded it. > end-of-line convention (postscript is ASCII and that file has the > unix end-of-line convention). -- No problem. Groetjes, Wim de Lange _____________________________________ Internet: wdelange@biochem.nl CompuServe: 100142,604 _____________________________________ - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Thu, 3 Sep 1998 05:52:48 -0400 From: Sylvie Gallet Subject: (fractint) Sylvie's site Hi Christian, >> I had problems though with accessing Gallet_c.zip, Gallet_d.zip and >> wallpapr.zip and the vesa2cfg link. AOL answered with a simple 'URL >> not found'. It was a problem with case sensitive filenames, it's fixed. Cheers, - Sylvie - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Thu, 03 Sep 1998 06:55:58 -0500 From: Elaina Tillinghast Subject: Re: (fractint) New Images on Web Well a couple of things got in the way of me getting to my web pages... The preferrence of what size image is most favored was split equally down the middle between 640x480 and 1024x768. Either you want all to fit on one screen quickly or you want all the detail you can get. I thank all those people who took time to write. The results are in favor of 640x480 since bigger would make it so many could not see them at all. Then if space isn't a problem, BIG! as a choice for those who can handle it. Juice -have fun --harm none - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Thu, 3 Sep 1998 13:43:39 +0100 From: Dave Subject: (fractint) Posting fractal images on the web I've noticed that many pages showing each fractal pattern tend to have ALL images as huge GIFs on the title page. Wouldn't it be a better idea to: a) have thumbnails linking to the larger picture, so that you can browse through ALL images from the title page and select the one you want to see in full splendor b) Store the larger versions as .JPEGs, thus permitting a full range of colours but keeping the filesize of the images down. This allows the images to be downloaded quickly, but I don't know what impact it has on the overall quality of the picture c) have perhaps two different links under each thumbnail, pointing to 640x480 or 1024x768-sized images, thus satisfying resolution requirements of both parties. (But it'd mean reconstruction of each image at different resolutions, or resizing/resampling in an imaging package - is this feasible?) I realise many people are still starting out in HTML, and fall into the pitfall of not realising that what appears instantly when browsed locally takes much longer when viewed via a modem. As a test, try flushing your web browser cache and then view your pages via your ISP to see how long they take to come down. Any views on this, people? > ---------- > From: Elaina Tillinghast[SMTP:juice@airmail.net] > Reply To: fractint@lists.xmission.com > Sent: 03 September 1998 12:55 > To: fractint@lists.xmission.com > Subject: Re: (fractint) New Images on Web > > Well a couple of things got in the way of me getting to my web > pages... > > The preferrence of what size image is most favored was split equally > down the middle between 640x480 and 1024x768. Either you want all to > fit > on one screen quickly or you want all the detail you can get. > > I thank all those people who took time to write. The results are in > favor of 640x480 since bigger would make it so many could not see them > at all. Then if space isn't a problem, BIG! as a choice for those who > can handle it. > > Juice -have fun --harm none > > -------------------------------------------------------------- > Thanks for using Fractint, The Fractals and Fractint Discussion List > Post Message: fractint@lists.xmission.com > Get Commands: majordomo@lists.xmission.com "help" > Administrator: twegner@phoenix.net > Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" > - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Thu, 03 Sep 1998 08:08:26 -0700 From: "Angela Wilczynski" Subject: Re: (fractint) Posting fractal images on the web Dave wrote: > > I've noticed that many pages showing each fractal pattern tend to have > ALL images as huge GIFs on the title page. > > Wouldn't it be a better idea to: > > a) have thumbnails linking to the larger picture, so that you can browse > through ALL images from the title page and select the one you want to > see in full splendor For some of us with many fractals on display, even thumbnails of ALL the images create an introductory page that is too slow to download. I am a very firm believer in paying great attention to bandwidth, particularly on the introductory page. Most surfers will go on to something else if the intro page doesn't show it's stuff in less than a minute. Fortunately, not everything need be displayed at once....only enough material to pique interest. > b) Store the larger versions as .JPEGs, thus permitting a full range of > colours but keeping the filesize of the images down. This allows the > images to be downloaded quickly, but I don't know what impact it has on > the overall quality of the picture Storing Fractint images as jpgs destroys the information that is bundled with the image and which can be used after the gif is downloaded and opened in Fractint. So moving to jpg is, for me, a matter of deciding which audience I want to please most....the one with limited time or patience or my Fractint collegues. Also, I find conversion from gif to jpg is sometimes unsatisfying in terms of how the image looks. > c) have perhaps two different links under each thumbnail, pointing to > 640x480 or 1024x768-sized images, thus satisfying resolution > requirements of both parties. (But it'd mean reconstruction of each > image at different resolutions, or resizing/resampling in an imaging > package - is this feasible?) > This is basically a lot of work and assumes one has a great deal of space available and can choose to store the same image twice. A more practical solution is one many on the list use......provide the image as a jpg and as a par file. Angela - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Thu, 3 Sep 1998 11:08:41 EDT From: RParracho@aol.com Subject: Re: (fractint) Understanding Formulas In a message dated 02-09-98 3:41:05 PM EST, kchildre@uccs.jpl.nasa.gov writes: << I've been experimenting with formulas and pars done by those on the list and ones that I've found here and there for several weeks now. Something that has been intriguing me is how do people come up with the formulas and coloring methods that they do? >> Ken, If you want some good starting places pick up a Calculus and Analytical Geometry book at a library or flea market. As you go through it you'll find lots of equations to plug into an escape type fractal. If you look at 'series' their convergence and divergence and what separates the two and remainder theory it'll give you more ideas. Then the next book you could look for is one on comnplex analysis and conformal mapping. things are very different in the complex plane. I'm relatively new to the IF...ENDIF logic and I haven't done much with it. This tool gives you precision control over the coloring method but a lot of mathematical up front work is required. As a basic rule of thumb when you iterate you can track three basic values: the count at which you are at, the value which you are at, and the location in your coordinate system (cartesian, polar, etc). by establishing standards of comparison for those values you have come up with a new unique coloring /rendering method. Unfortunately its been my experience that to rigorous a standard makes your fractals look plain and lousy. Always be willing to test your standards boundry because thats where it gets great. for instance (off the top of my head) say we want to test our iteration based on count and value so that as count increases we begin to loose grasp of the original value(kind of like hiesenberg). z=current value n= iteration count c=arbitrary constant: conditional test: |z|<= (c+z/n)^n try the conditional >= (half the time things get exciting around zero the other half infinity) change the arbitrary constant to extremes make n a function of iteration n=F(iter#) etc. Can I begin to see where this is going. NO! but I'm pretty familiar with how the M-set behaves so I'll iterate that function with this test first and see what it does to the that behavior. Try halley maps in regions that f'(z)>f(z) (divergent areas). Try halley maps on functions with singularities or discontinuity And best of all, it can turn out to be just junk or it could be a surprise. I hope this helps. This thought process is chaotic like my explanation. Good luck Rui - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Thu, 03 Sep 1998 10:49:37 -0500 From: "Damien M. Jones" Subject: Re: (fractint) Posting fractal images on the web [Reply to Angela is below this one.] Dave, - a) have thumbnails linking to the larger picture, so that you can browse - through ALL images from the title page and select the one you want to - see in full splendor Yes, but this is still not an optimal solution if you have a lot of pictures. Right now I've got two layers of thumbnails before you get to the actual pictures. Few people want to download a page with 200+ thumbnails on it. - c) have perhaps two different links under each thumbnail, pointing to - 640x480 or 1024x768-sized images, thus satisfying resolution - requirements of both parties. (But it'd mean reconstruction of each - image at different resolutions, or resizing/resampling in an imaging - package - is this feasible?) It does indeed mean resizing the images more than once, but if you're preparing thumbnails, you're already preparing more than one size. For example, I typically generate my images at 1600x1200 or 1280x960; these are then resized down to 640x480 and saved (large size), resized to 128x96 and saved (thumbnail), and a few resized to 200x150 and saved (larger thumbnail for the main gallery index). I *could* have also prepared 1024x768 versions of these images, but when I started my gallery space was a concern; space is no longer a problem for me, but the sheer quantity of images *is*. I'm not sure I want to take the time to prepare 1024x768 versions of so many pictures. - Any views on this, people? Don't get me started. :-) Angela, - Storing Fractint images as jpgs destroys the information that is bundled - with the image and which can be used after the gif is downloaded and - opened in Fractint. This may or may not be a drawback, depending on your viewpoint. Personally, I'd say go for the JPEG anyway, and provide a PAR file for those that want parameters. It's usually worth the savings. - Also, I find conversion from gif to jpg is sometimes unsatisfying in - terms of how the image looks. Well, you *know* I'm going to say that doesn't have to be the case. :) Generate your image at large size and reduce it (for anti-aliasing) and then save in JPEG format with appropriate settings. - This is basically a lot of work and assumes one has a great deal of - space available and can choose to store the same image twice. A more - practical solution is one many on the list use......provide the image as - a jpg and as a par file. And although I just advocated the JPEG+PAR approach, there are situations where it isn't appropriate--particularly, cases where the image has been post-processed in some fashion outside of FractInt, or produced with a custom program that isn't generally available. Or cases where you really don't feel like giving out the PAR file. :-) Damien M. Jones \\ dmj@fractalus.com \\ Fractalus Galleries & Info: \\ http://www.fractalus.com/ - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Thu, 03 Sep 1998 12:32:17 -0500 From: "Damien M. Jones" Subject: (fractint) Just two days left! Greetings listfolk, There are just two days left for you to submit your entries to the Fractal Art '98 Contest. Scores of entries have already been received; we certainly appreciate the number of entries (more than last year's contest!) and the exceptional quality and variety. If you have not already submitted three images, the deadline is fast approaching--no further entries will be accepted after 10PM PDT, September 5. (That's Saturday night!) We'd certainly like you to enter! You can find all the details--rules, categories, and so on--at the contest web site: http://www.fractalus.com/contest98/ Damien M. Jones \\ dmj@fractalus.com \\ Fractalus Galleries & Info: \\ http://www.fractalus.com/ - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Thu, 3 Sep 1998 18:20:42 +0100 From: Dave Subject: RE: (fractint) Posting fractal images on the web > For some of us with many fractals on display, even thumbnails of ALL > the > images create an introductory page that is too slow to download. Ah - crossed wires here. I looked at one webpage last week that had about 6 full-sized pictures on it. I just thought it would have been a better idea to reduce these to thumbs, thus getting a summary of what to expect downloaded quickly. I didn't mean that I wanted everyone to fill their title pages with thumbs of ALL of their current images!! But for those with many fractals on display, surely thumbnails of them on an intgro page is quicker to download than a page containing all of the displays? > I am a > very firm believer in paying great attention to bandwidth, > particularly > on the introductory page. Most surfers will go on to something else > if > the intro page doesn't show it's stuff in less than a minute. > Fortunately, not everything need be displayed at once....only enough > material to pique interest. Agreed. Perhaps categories of thumbs from an index page, etc.... > > b) Store the larger versions as .JPEGs, thus permitting a full range > of > > colours but keeping the filesize of the images down. This allows the > > images to be downloaded quickly, but I don't know what impact it has > on > > the overall quality of the picture > > Storing Fractint images as jpgs destroys the information that is > bundled > with the image and which can be used after the gif is downloaded and > opened in Fractint. So moving to jpg is, for me, a matter of deciding > which audience I want to please most....the one with limited time or > patience or my Fractint collegues. Also, I find conversion from gif to > jpg is sometimes unsatisfying in terms of how the image looks. > .. but surely your fract colleagues would prefer the formulae with which you created the image, rather than reverse-engineer the GIF? I'm still new to this game, but I had problems extracting image info from a GIF I was given. > > c) have perhaps two different links under each thumbnail, pointing > to > > 640x480 or 1024x768-sized images, thus satisfying resolution > > requirements of both parties. (But it'd mean reconstruction of each > > image at different resolutions, or resizing/resampling in an imaging > > package - is this feasible?) > > > > This is basically a lot of work and assumes one has a great deal of > space available and can choose to store the same image twice. A more > practical solution is one many on the list use......provide the image > as > a jpg and as a par file. True, but I'm looking at it from the point of view that "the more effort put in by the one writer, the less effort required by the many readers". Perhaps it's a selfish view, I don't know. As for the space available, the JPEG+PAR solution sounds a much better idea. Would two JPEGs of the same image require less storage space than one GIF? - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Thu, 03 Sep 1998 20:48:48 -0700 From: "Angela Wilczynski" Subject: Re: (fractint) Posting fractal images on the web Dave wrote: > > > .. but surely your fract colleagues would prefer the formulae > with which you created the image, rather than reverse-engineer the GIF? > I'm still new to this game, but I had problems extracting image info > from a GIF I was given. > > This is basically a lot of work and assumes one has a great deal of > > space available and can choose to store the same image twice. A more > > practical solution is one many on the list use......provide the image > > as > > a jpg and as a par file. > True, but I'm looking at it from the point of view that "the more effort > put in by the one writer, the less effort required by the many readers". > Perhaps it's a selfish view, I don't know. As for the space available, > the JPEG+PAR solution sounds a much better idea. Would two JPEGs of the > same image require less storage space than one GIF? Let's see...... 1. Regarding the gif versus jpg question........I believe that I am often doing everyone a favor by posting a largish gif with the Fractint info in tact rather than the par (or at least in addition to the par) because the par could take faaaaaaaaaaar longer to generate than the gif does to download. That is always a consideration for me. In general I like the jpg + par approach because I feel more comfortable that my images will be treated with care by my Fractint bretheren. I figure the jpg's....regardless of the copyright babble......will be pilfered. That is certainly another consideration in how I post my images......I give up the really good stuff to the web with great reluctance. 2. Dealing with the gif in fractint is simplicity itself.....put the gif where you can reasonably locate it...the most basic spot being where fractint resides....open the gif using "r" then save the parameters by hitting that old "b". You can zoom into or out of the fractal at will right from the gif or use Paul Carlson's great hint of hitting z for the parameters, then F6 and enter a couple of times. I hope I have that right as I haven't done it in a while. At any rate.....you can return to the "original" image using the gif parameters in that way then start on your own journey. That is my fav thing to do. 3. Space limitations are space limitations...period. If one doesn't have space available to post (and most don't) the dual posting is not an option. I consider my time and space far more valuable than that of web surfers who are a non-paying audience which MUST be considered because "their" download minutes will cause them annoyance......I refuse to cost myself hours of effort or more $$ for web space for their minor inconvenience when they are getting a freebie. One is not required to pander to all wishes. I try to make reasonable compromises. I have in excess of 35 megs of "stuff" on the web so managing it takes considerable time already. Maybe those whose jobs are connected with the web or who have smaller websites can more profitably use your suggestions. Angela - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Thu, 03 Sep 1998 22:13:19 -0700 From: kathy roth Subject: (fractint) Understanding Formulas Hi math-ophiles. This discussion has been very interesting. I have been clumping around getting some understanding of the basics and am getting an appreciation for the leap of thought it takes to think of something new, not so much how you write the formula but the imagination in thinking of the orbit traps, stalks and the flexballs, bubbles and triangles and all that. It's very creative. I was reading about Julia and Fatou. Early in this century they visualized all this (or a good part of this) and never lived to see it on a screen and certainly not in 256 colors. I wonder if it was totally an abstraction or if they could visualize it somewhat. They never knew what it looked like or saw all these people developing things from it. (or.....who knows....) Anyway, I have some basic questions that I have not been able to figure out using the references from this list. Some of it is math but I think more of it is programming or just knowing the conventions of the If..Else formulas. I've read (partially!) the Devaney and Peitgen books and some things on chaos etc. and am at roughly an advanced high school or college math for non-math major sort of level. Ummm, so- basic math question on popcorn_jul and complex numbers: Popcorn_Jul popcorn_jul { ; Paul Carlson, 1998 ; Always use float=yes ; ; real(p1) = h in popcorn formula ; imag(p1) = bailout value ; x = real(pixel) y = imag(pixel) h = real(p1) : prev_x = x x = x - h * sin(y + tan(3 * y)) y = y - h * sin(prev_x + tan(3 * prev_x)) z = x + flip(y) |z| <= imag(p1) } I thought this was about separating the x and y pixel in the initialization and then iterating the Julia formula. But does x = x - h * sin(y + tan(3 * y)) y = y - h * sin(prev_x + tan(3 * prev_x)) have something to do with z^2 + c? I thought I could figure this out with the "Formulae for Complex Numbers" but couldn't. (Actually I do not get for example why e^z=e^x(cosy + i*siny). Would this be in an Analytical Geometry text?) Similarly, I always liked conic sections and graphs in school and was looking at Kerry Mitchell's conic section formulas. conic { ; Kerry Mitchell 12may98 ; ; draws conic sections, not fractals ; Ax^2 + Bx + Cy^2 + Dy + Exy + F = 0 ; A=real(p1), B=imag(p1), C=real(p2), D=imag(p2) ; E=real(p3), E=imag(p3). use decomp=256 coloring ; a=real(p1), b=imag(p1), c=real(p2), d=imag(p2) e=real(p3), f=imag(p3), iter=-1: x=real(pixel), y=imag(pixel) t=x*(a*x+b)+y*(c*y+d)+e*x*y+f t=log(cabs(t)) z=cos(t)+flip(sin(t)) iter>0 } I understand the Ax^2 + Bx parts. Where did the " t=log(cabs(t)) z=cos(t)+flip(sin(t))" come from? Thanks! Sorry about the length of this- Kathy - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Thu, 03 Sep 1998 22:35:05 -0700 From: kathy roth Subject: (fractint) Understanding Formulas More formula questions! I think I understand the basics of the If..Else tutorial and understand bailout. But the If..Else formulas have phrases like: "bailout == 0 && |w| < 4" Bailout isn't actally 0, this seems like a language that I don't know. - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Tue, 01 Sep 1998 14:32:17 +0200 From: Guy Marson Subject: Re: (fractint) Fractal Risks? Hi Albert, At 11:22 31.08.1998 -0400, you wrote: >I am also interested in Amateur Radio, enjoy FRACTINT, it's a good antenna to the soul! >drawing, painting and carving. >I am 71 and am really starting to enjoy life. Keep up the good >work. Albert > 73's from LX1GM, Guy >-------------------------------------------------------------- >Thanks for using Fractint, The Fractals and Fractint Discussion List >Post Message: fractint@lists.xmission.com >Get Commands: majordomo@lists.xmission.com "help" >Administrator: twegner@phoenix.net >Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" > - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 4 Sep 1998 00:21:15 -0700 (MST) From: Kerry Mitchell Subject: Re: (fractint) Understanding Formulas On Thu, 3 Sep 1998, kathy roth wrote: > Ummm, so- > basic math question on popcorn_jul and complex numbers: > > Popcorn_Jul > popcorn_jul { ; Paul Carlson, 1998 [snippage] > x = real(pixel) > y = imag(pixel) > h = real(p1) > : > prev_x = x > x = x - h * sin(y + tan(3 * y)) > y = y - h * sin(prev_x + tan(3 * prev_x)) > z = x + flip(y) > |z| <= imag(p1) > } > I thought this was about separating the > x and y pixel in the initialization and then iterating > the Julia formula. But does > x = x - h * sin(y + tan(3 * y)) > y = y - h * sin(prev_x + tan(3 * prev_x)) > have something to do with z^2 + c? Paul is separating x and y and iterating them independently. However, this is *not* the familiar z^2+c formula. That would look like this: x = x*x - y*y + real(c) y = 2*prev_x*y + imag(c) Where the "prev_x" variable is used to force the y equation to use the previous iteration's value of x, instead of the newly computed one in the x formula. I don't know if Paul's Popcorn formula has an easy expression in terms of z. If it did, he'd probably use it. > couldn't. (Actually I do not get for example > why e^z=e^x(cosy + i*siny). Would this be in an > Analytical Geometry text?) This should be easily found in a complex analysis text. Basically, for any angle theta, exp(i*theta) = cos(theta) + i*sin(theta). *Why* this is depends on whose perspective you take, so it might just be easier right now to accept it. Then, exp(z) = exp(x+i*y) = exp(x)*exp(i*y) = exp(x)*[cos(y) + i*sin(y)]. This comes about from the rules of exponents (a^(b+c) = a^b * a^c) and the exp(i*theta) expression above. > Similarly, I always liked conic sections and graphs > in school and was looking at Kerry Mitchell's > conic section formulas. [more snippage] > I understand the Ax^2 + Bx parts. Where did > the > " t=log(cabs(t)) > z=cos(t)+flip(sin(t))" come from? Two parts: first, I use "t" as a temporary variable to hold the result of the conic section calculation. If t=0, then the iterate is right on the section. Since that will not happen very often, I want to highlight those points "close" to the section, to show where it is. I often do that by using a log transform: log(t) goes to negative infinity very quickly as t goes to zero (from above, through postive numbers. Use the cabs(t) to make sure that the argument is positive, since I don't want imaginary numbers at this point). Part 2 is to use this transformed t as an angle. z = cos(t) + flip(sin(t)) is the same as z = cos(t) + i*sin(t), or z = exp(i*t). So, when I use Fractint's "decomp=256" coloring, that will show narrower and narrower bands of color as the (original) t goes to zero, or as the iterate gets closer to the section. Simple, right? :-) Anyway, you now have a little bigger window into my twisted world of coloring scheme development, and hopefully, a little better understanding of the math and programming behind them. Kerry Mitchell - ------------------------------------------------------------------------------- Kerry Mitchell lkmitch@primenet.com www.primenet.com/~lkmitch/ - ------------------------------------------------------------------------------- - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 4 Sep 1998 00:26:30 -0700 (MST) From: Kerry Mitchell Subject: Re: (fractint) Understanding Formulas On Thu, 3 Sep 1998, kathy roth wrote: > More formula questions! I think I understand the > basics of the If..Else tutorial and understand > bailout. But the If..Else formulas have phrases like: > > "bailout == 0 && |w| < 4" This means, "bailout equals 0 and magnitude of w is less than 4". The "==" means "is it equal to?", as opposed to "=", which means, "set it equal to". "&&" means "and", but the Boolean kind, where if the statement "a && b" is true, then both "a" and "b" have to be true. The Boolean "or" is "||". The rest is fairly standard formual stuff--checking the magnitude of a complex number to see if it's smaller than some threshold. Kerry Mitchell - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 4 Sep 1998 10:19:03 -0400 (EDT) From: kragen@pobox.com (Kragen) Subject: Re: (fractint) Understanding Formulas On Fri, 4 Sep 1998, Kerry Mitchell wrote: > On Thu, 3 Sep 1998, kathy roth wrote: > > "bailout == 0 && |w| < 4" > > This means, "bailout equals 0 and magnitude of w is less than 4". The I'm confused. I thought |w| meant the square of the magnitude of w, not the magnitude of w itself. Kragen (a formula newbie) - -- Kragen Sitaker I don't do .INI, .BAT, .DLL or .SYS files. I don't assign apps to files. I don't configure peripherals or networks before using them. I have a computer to do all that. I have a Macintosh, not a hobby. -- Fritz Anderson - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 4 Sep 1998 07:22:34 -0700 (MST) From: Kerry Mitchell Subject: Re: (fractint) Understanding Formulas You're right. My bad. Thanks. - ------------------------------------------------------------------------------- Kerry Mitchell lkmitch@primenet.com www.primenet.com/~lkmitch/ - ------------------------------------------------------------------------------- On Fri, 4 Sep 1998, Kragen wrote: > On Fri, 4 Sep 1998, Kerry Mitchell wrote: > > On Thu, 3 Sep 1998, kathy roth wrote: > > > "bailout == 0 && |w| < 4" > > > > This means, "bailout equals 0 and magnitude of w is less than 4". The > > I'm confused. I thought |w| meant the square of the magnitude of w, > not the magnitude of w itself. > > Kragen (a formula newbie) > > -- > Kragen Sitaker > I don't do .INI, .BAT, .DLL or .SYS files. I don't assign apps to files. I > don't configure peripherals or networks before using them. I have a computer > to do all that. I have a Macintosh, not a hobby. -- Fritz Anderson > > > -------------------------------------------------------------- > Thanks for using Fractint, The Fractals and Fractint Discussion List > Post Message: fractint@lists.xmission.com > Get Commands: majordomo@lists.xmission.com "help" > Administrator: twegner@phoenix.net > Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" > - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 4 Sep 1998 12:23:46 -0400 From: "Marie Drozdis" Subject: RE: (fractint) Understanding Formulas Please don't use this list to start a platform war. Thank you. - -----Original Message----- From: owner-fractint@lists.xmission.com [mailto:owner-fractint@lists.xmission.com] On Behalf Of Kragen Sent: Friday, September 04, 1998 10:19 AM To: fractint@lists.xmission.com Subject: Re: (fractint) Understanding Formulas Kragen Sitaker I don't do .INI, .BAT, .DLL or .SYS files. I don't assign apps to files. I don't configure peripherals or networks before using them. I have a computer to do all that. I have a Macintosh, not a hobby. -- Fritz Anderson - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 04 Sep 1998 13:04:11 -0400 From: Diosnel Herrnsdorf Subject: Re: (fractint) Understanding Formulas > (Actually I do not get for example > why e^z=e^x(cosy + i*siny). Would this be in an > Analytical Geometry text?) Hi, Kathy. I don't think I'm able to give an answer for most of your questions. However, I'll give you this one. First of all, remember that z=x+i*y, where i=sqrt(-1). Now, you can write e^z=e^(x+i*y)=e^x*e^(i*y). The first part of the product comes into the formula. The second part comes from Euler's identity: e^(i*y)=cosy+i*siny. You can reach it with Taylor's series. If you express cosy, i*siny and e^(i*y) as series, you will get the identity. You see that the answer is more in calculus than in analytical geometry, though I think there should be some little explanation in the preliminars of complex numbers. I hope this is not too dark (this is the first time I'm thinking math in English) and helps you understand it a little.:-) Regards, Diosnel - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ End of fractint-digest V1 #288 ******************************