User talk:Rocchini

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Welcome!

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

I hope you enjoy editing here and being a Wikipedian! Please sign your name on talk pages using four tildes (~~~~); this will automatically produce your name and the date. If you need help, check out Wikipedia:Questions, ask me on my talk page, or ask your question and then place {{helpme}} before the question on your talk page. Again, welcome! Oleg Alexandrov (talk) 03:41, 8 August 2007 (UTC)

[edit] Rose

Hey Rocchini. Just wanted to say "well done" with that graphic for the Rose. It looks really nice. Cheers, Doctormatt 08:36, 6 November 2006 (UTC)

[edit] Cat

Chapeau Claudio! Nice contribution to the article Arnold's cat map. JocK 19:14, 9 November 2006 (UTC)

Once more a request for your artistic talents... You might be interested in another visualisation of the chaos occuring in simple discrete maps like Arnold's cat map. If you take - say - a 50 x 50 integer grid, and start iterating the cat-map on that grid to obtain the various closed trajectories, and color each distinct trajectoru differently, a nice colourful plot is obtained. See http://base.google.com/base/a/jkoelm/1121639/6838743187121338456 for a similar picture for another integer 2D-map (as you can see: my graphics skills aren't anywhere close to yours). Cheers, JocK 21:18, 8 August 2007 (UTC)

[edit] Dipole graph

I just wanted to thank you for the image you added to Dipole graph. I've been meaning to make one but couldn't find a nice tool to do it with--and my skill at MS Paint isn't sufficient for the task. Do you mind if I ask what tool you used to make the image? I'd like to be better prepared in the future. --Sopoforic 05:00, 28 November 2006 (UTC)

[edit] Spherical cap

Excellent job on the image, it helps the article, and I appreciate it. The same for your other math images. —Ben Brockert (42) 05:45, 29 November 2006 (UTC)

[edit] SVG

I asked previously which tools you use to create images, and you recommended Inkscape, which I have found quite satisfactory. I notice, though, that you've been uploading your images in GIF format. If you've still got the SVGs you used to make those images, you should upload them directly, since they'll look much nicer, and be more useful besides. If you've not got them, you should still keep it in mind for the future. Thanks for your work, in any case. --Sopoforic 01:46, 10 January 2007 (UTC)

[edit] Honeycomb images

Hi! Great images for the uniform polychorons. I've been expanding the Coxeter-Dynkin diagram. I also saw your rcent nice cell-uniform tessellation at Disphenoid tetrahedral honeycomb. I'm wondering if you could make a similar tessellation image for the dual of: Cantitruncated cubic honeycomb. I don't have a name for it, but this tetrahedral space-filling dual should represent the fundamental domains for Coxeter's S₄ infinite group. Does this make sense? I'm still getting the hang of things. Thanks for considering! Tom Ruen 06:24, 24 January 2007 (UTC)

Hey! I have to agree these images are amazing, I'm using the Order-3 for my background. I was just wondering what program you used, it looks very professional and at the moment all I'm using is GIMP and Inkscape. Aragan Jarosalam

I use my mathematical C++ class library wich exports the results in vrml format (for preview) and POV Ray format (for final version of images). (Quasi) all images of my gallery are done with my library. Rocchini.

[edit] excellent image at braid theory

I will certainly remember you for the next time I need a nice image! --C S (Talk) 13:38, 28 January 2007 (UTC)

[edit] Hyperbolic tilings

Hi Rocchini!

Great new images on Hyperbolic great cubic honeycomb!

I've also been wishing to expand the 2d hyperbolic tiling as well, but I don't have software that can generate the uniform duals: See blanks at List_of_uniform_planar_tilings#Uniform_tilings_in_hyperbolic_plane

They are all similar topology to the Euclidean tilings. Coloring the duals is unclear since they have identical faces. I wouldn't even mind if they are single-colored faces with dark edges.

Maybe they are "too easy" for you, but it thought I'd ask. I'm glad for where ever you can help!

Tom Ruen 23:15, 5 February 2007 (UTC)

for a moment I have made the common image Order3_heptakis_heptagonal_til.png

but I not undestand how to insert in the List_of_uniform_planar_tilings#Uniform_tilings_in_hyperbolic_plane page. Because in the original tilining the color is per face, in the dual tiling I have colored the surface per vertex.

Thanks Rocchini! Sorry on the template confusion. The source (database) is at: Template:Uniform_hyperbolic_tiles_db. I added it for your example. I don't mind how it is colored, although best to have a full set of vertex-colorings if you could repeat them all that way. Thanks again! (I also linked image at Triangular_tiling) Tom Ruen 21:07, 7 February 2007 (UTC)

Can you make the nonreflective snub form duals? Explained a bit here for a flat tiling: Snub_square_tiling - creating an omnitruncation and then delete alternated vertices? Don Hatch does this in an interesting way in an Applet at Hyperbolic Planar Tesselations by Don Hatch but no colors. Tom Ruen 21:13, 7 February 2007 (UTC)

Wonderful work! Thanks! I thought tonight the (5 4 2) family would be a useful example as well betond the (4 4 2) tilings. Could you try those as well? I left open image links at:List_of_uniform_tilings#.285_4_2.29_family. Tom Ruen 07:42, 10 February 2007 (UTC)

Hi Rocchini. Thanks again for your great images. I saw I made a mistake on omnitruncated dual tiling names, not a kis operation. I replaced it with term bisected for (5 4 2) group (Image:Order-4 bisected pentagonal tiling.png) and will update the rest when I have time. So at least you can continue on List_of_uniform_tilings. Thanks again! Tom Ruen 02:36, 14 February 2007 (UTC)

Wow! All so beautiful! I found one more family to complete a good demonstrational survey of the hyperbolic tilings

Euclidean --> hyperbolic

(6 3 2) --> (7 3 2) - Hexagonal/heptagonal (DONE)

(4 4 2) --> (5 4 2) - Square/pentagonal (DONE)

(3 3 3) --> (4 3 3) - Triangular/square (started)

What do you think of the last one? I just linked (4 3 3) at List of uniform tilings. Tom Ruen 23:05, 15 February 2007 (UTC)

I suppose that a nice coloring rule of duals is related to some property of the tessellation (Symmetry group?), but i not understand how. User:rocchini 20 February 2007 (UTC)

I don't have a simple rule for coloring dual faces by symmetry. Since they are all face-transitive, the lowest coloring is ONE color! There's probably many colorings for each limited by the symmetry orders. It is nice when all neighboring faces are different colors. Your choices have been beautiful! :) Tom Ruen 18:06, 20 February 2007 (UTC)

A small issue: The Image:Uniform dual tiling 433-t01.png tiling is a wonderful 3-color pattern, but incompletely applied near edges. I tried to fix it but couldn't do it nicely with antialiasing. Tom Ruen 19:14, 20 February 2007 (UTC)

Hi Rocchini. Looks like you're busy, me too! I just thought to add a simple white tiling image for the final snub (Image:Uniform dual tiling 433-snub.png) would be great whenever you have the time. Thanks! Tom Ruen 07:46, 28 February 2007 (UTC)

Thanks for finishing the last hyperbolic dual snub tiling. I had one other snub I couldn't make easily on a larger uniform survey (without duals) at Wythoff symbol - need Image:Uniform_tiling_443-snub.png similar to Image:Uniform_tiling_433-snub.png. I left an open link for it at Wythoff symbol.

I'm also very glad for more 3D hyperbolic tilings too! It would be fun to try some truncated versions, like table at Truncation_(geometry)#Truncation_in_polychora_and_honeycomb_tessellation ... probably need an "inside perspective" to show them. Tom Ruen 23:52, 1 March 2007 (UTC)

I have worked 5 days (and povray 12hours) for this hyperbolic awful image. I try to remake it in the next week.

I don't know how you do any of it, and it all seems beautiful to me. Much glad for your work. Peace and thank you! Tom Ruen 10:01, 2 March 2007 (UTC)

[edit] Image:Cayley graph formula 2 4.gif listed for deletion

An image or media file that you uploaded or altered, Image:Cayley graph formula 2 4.gif, has been listed at Wikipedia:Images and media for deletion. Please look there to see why this is (you may have to search for the title of the image to find its entry), if you are interested in it not being deleted. Thank you. – Tintazul ^msg 23:42, 20 February 2007 (UTC)

I have to add: you make such wonderful images for Wikimedia! Thank you for that. Although I should ask, if whenever possible, you could make those images available in vector format. I use Inkscape, which ias fairly easy to use. This is the case now: I have redrawn your image completely in SVG, keeping to the original colours and structure as much as possible. If you have any doubts, please contact me. Ciao! – Tintazul ^msg 23:42, 20 February 2007 (UTC)

Thanks for this work! I generate the original image via agg graphics library (this library save only raster image), and i am too much lazy to remake this image.

[edit] Hypercube graphs?

Hi Rocchini! If you'd like a little challenge for your to-do list, I'd like to flesh out some graphs for the n-hypercubes, like done for the simpler families: simplex and cross-polytope. Mathworld offers some graphs, although I do NOT know the pattern for adding "rings" of new vertices - maybe lots of possibilities? See:[[1]]. Well, just thought I'd point it out. I could try myself sometime since graphics is easy, but theory of positions a mystery. I added a hexeract stub along with penteract. Hey, another source of graphs [2] - maybe they're actually certain views of an orthogonal projection? Tom Ruen 06:39, 16 March 2007 (UTC)

Wow! Thanks! You're fast! If you're interested another fun class are the demihypercubes. I added a graph column there. Tom Ruen 19:57, 16 March 2007 (UTC)

[edit] E6,7,8 graphs?

Hi Rocchini! Thanks for the hypercube/demi graphs. What do you think of the E6 polytope {3^2,2,1}, E7 polytope{3^3,2,1}, E8 polytope {3^4,2,1} graphs? I have pictures from a book, but don't really understand the structures. Can you reproduce these in SVG? Image:E6_graph.png, Image:E7-8 graphs.png Tom Ruen 08:40, 26 March 2007 (UTC)

Example of E8 drawing at: [3] (dense!) Tom Ruen 01:44, 27 March 2007 (UTC)

As you see, I have not understood the argument. How to compute the root adjacency? User:Rocchini 2007-04-26.

Hey Rocchini, no problem. I don't know how to compute them either. I just hoped you might. :)Maybe I can find some source code that plots them sometime. Thanks again, and keep up with the great graphs and pictures! Tom Ruen 16:47, 26 April 2007 (UTC)

This is e6, e7, e8 in svg format Image:E6_graph.svg, Image:E7_graph.svg, Image:E8 graph.svg. It is correct? User:Rocchini 2007-06-04

Thanks! Looks very good to me. I'm very glad for these nice additions. I added labels to the article picture captions. Tom Ruen 16:19, 4 June 2007 (UTC)

[edit] Kudos

Kudos for all your wonderful images! (from an old friend that has just discovered you as a wikipedian) ALoopingIcon 23:31, 16 April 2007 (UTC)

[edit] Moving sofa problem

Hi Rocchini, you might want to have a look at Moving sofa problem. It would be great if you could create an animated gif that shows a 'telephone shaped' sofa moving through a right-angle corridor. I don't think such a graphics is available anywhere on the internet. Cheers, JocK 17:46, 25 May 2007 (UTC)

I try this:

, User:rocchini 28 may 2007 (UTC).

Again a fantastic piece of graphics! Many thanks, JocK 10:58, 28 May 2007 (UTC)

[edit] Complex analysis

Thank you for the awesome picture at Complex analysis. It is just great! Oleg Alexandrov (talk) 03:41, 8 August 2007 (UTC)

[edit] A further comment on pictures

As many people have noticed, you are creating really awesome pictures. I have a suggestion. Would it be possible for you to include the source together with each picture? I, for example, would be very interested in learning from you, and I am sure I am not the only person. Thanks. You can reply here. Oleg Alexandrov (talk) 06:39, 8 August 2007 (UTC)

Thanks for comments and suggestion. I have the same idea, but this "thing" is not so easy. The "source" of each image is a mix of C++ source code plus external library (like AGG graphics), shell script, Blender and POV-Ray scripts, manual adjustments ans so on. My idea is to make, for each image, a "making of" page of the image. I do not know which location is the better place for these pages (wikipedia or a private personal site). I am working on. Rocchini 08:55, 9 August 2007 (UTC)

Any of this information can go on the picture page, for example, on commons:Image:Color complex plot.jpg, under the picture itself. Of course, if it is a lot of work to make the source public, and if you prefer to make new pictures rather than spend time writing about how you made the current pictures, that is understandable. Cheers, Oleg Alexandrov (talk) 16:09, 9 August 2007 (UTC)

[edit] Hyperbolic sector

Thank you Rocchini for producing an appropriate graphic for hyperbolic sector. I have also used it on hyperbolic angle. I find your gallery spellbinding. Great art and science fused to one. Beginners in things hyperbolic will benefit from the hyperbolic sector graphic. with much appreciation, Rgdboer 22:28, 13 September 2007 (UTC)

Now you have done even more good work at Ultraparallel theorem and Hyperbolic coordinates. I would like to put a caption on the hyperbolic coordinate image, but it should indicate the level curve geometric means and the separation of radial lines by a uniform hyperbolic angle. The way they bunch up near the asymptote gives the impression that is appropriate for hyperbolic angle. Today there is no diagram at hyperbolic angle due to a recent unfortuate sequence of edits. The diagram there should be more detailed than the one at hyperbolic sector, since the article is developing the measure concept. I would suggest using the point (1.39561242, .7165313) as a basic unit from (1,1). Since this pair corresponds to the cube root of e, the area of the sector is one-third wing, if we take the basic area one angle as defining a wing. Degrees and radians are familiar circular angle measures, and the centuries of use of circular angle has made these units common language. To date, I know of no initiative to introduce a named unit to refer to a hyperbolic angle, yet in cases such as this a named unit would be useful. Without such language, one can speak of the powers of the 1.3956 pair, and about ten of these will fill an octant, getting dense near the asymptote. If you used some other hyperbolic angle unit to generate the image at hyperbolic coordinates, it would be good to see it in a caption.Rgdboer (talk) 23:30, 20 May 2008 (UTC)

[edit] Thanks for ctr. octag. # img.

Just wanted to say thanks for your Image:Centered octagonal number.svg on behalf of WikiProject Numbers. It looks very nice. Thanks for the image. PrimeFan 23:51, 7 October 2007 (UTC)

[edit] Image:Edge contraction.svg

Hello, I have replaced the arrows of this image with hand-drawn arrows because the arrowheads did not render properly due to a render-bug/limitation in wikipedia. If you want to see the bug you can revert to the old version at commons:Image:Edge_contraction.svg#file history. It does not look as good now, but at least it now shows properly in the article. ssepp^(talk) 16:54, 21 October 2007 (UTC)

Thank you for refinements! Rocchini 13:00, 22 October 2007 (UTC)

[edit] Image:Cayley's formula 2-4.svg

Hello, I have uploaded a new version of this image. In the old version ([4]) if we look at the trees with 4 vertices, then, referring to the trees in matrix notation, tree (1,1) and (2,2) are both red-yellow-green blue, and trees (1,3) and (3,2) are both blue-red-yellow-green. Trees with red-blue-green-yellow and yellow-red-blue-green were missing. In the new version I have fixed this. I hope it is ok now, it is easy to get confused working with this :). ssepp^(talk) 17:44, 21 October 2007 (UTC)

Thank you for refinements! Rocchini 13:00, 22 October 2007 (UTC)

[edit] Color Complex Plot Image

I was wondering what program you use to create your image for the Complex Numbers page. I've been looking for something that could plot things of that nature for quite a while, and I would be greatly appreciative if you could help me. Vjasper 20:49, 23 October 2007 (UTC)

I have added to image page the C++ source code for generating this image. You may change the FUN function to plot another complex function. Rmi, Rma, Imi, Ima represents the function domain. Rocchini 06:39, 25 October 2007 (UTC)

Thx for great image. Your method ( creating PPM file) is probably the simplest ( and effective) method of crating 2D 24 bit color graphic. I was looking for this for years and now I have found. Thx. I have made a simple example about it in Polish wikibook. Maybe it should be in new wbook about graphic/c ? Do you know something about flo files ? Regards --Adam majewski (talk) 07:58, 15 December 2007 (UTC)

[edit] Art gallery problem

Hello, I thought you might find it interesting to create an image for this article: Art gallery problem. Arthena 22:30, 29 October 2007 (UTC)

I try first sample image

. Rocchini 16:16, 30 October 2007 (UTC)

That's beautiful! Thank you! Just one thing: I think the bottom of the middle bottom room should just be green, not cyan, since the blue camera does not reach there. In other words, the right blue camera lacks a horizontal vision line. Arthena^(talk) 21:59, 30 October 2007 (UTC)

Argh! You have good eyes. Rocchini 16:41, 31 October 2007 (UTC)

[edit] Angle of parallelism

Thank you Rocchini for getting us a graphic on angle of parallelism. This old idea in geometry is so useful but illusive to those without a model to work on. You have brought the topic out of the shadows. Your contribution is a valuable scientific illustration. Rgdboer 20:37, 15 November 2007 (UTC)

[edit] Hypercubes and demihypercubes and 2n-gonal symmetry

Hi Rocchini. The new E8 animation graphics online [5] have inspired me to look at graphing the higher regular/uniform polytopes again.

I've not been successful yet, but thinking the n-hypercube ought to be orthogonally projectable into a regular 2n-gon. Just like the square (2-cube) is a 4-gon, cube (3-gon) projects in a hexagon, hypercube (4-cube) projects in an octagon, etc. This "projection" envelope represents a sort of zig-zag n-space path "circumference" around the figure. Similarly the n-demihypercube (hypercube with alternate vertices deleted) ought to be projectable into a regular n-gon. Well, the hard part is getting the correct "view plane" for this symmetry. The projections may not be "perfect" since there's overlapping vertices on the plane, but still nice for their symmetry, if it can be done.

The closest example I can find is on Mathworld [6], unsure how the graphs are made, and I don't think they are all pure projections, but maybe close.

Anyway, so far I just rewrote a n-cube generator, and can extend to make n-demicubes. I'd really like to try to get the n-cube/n-demicube graphs to correspond to each other (half the vertices in the second). Maybe I'll succeed, or maybe not.

If you'd like to try too, maybe you can follow my suggestions above and see if you can find a projection plane that has this 2n-gonal symmetry. I'll tell you if I make any progress!

Thanks! 20:16, 27 November 2007 (UTC)

[edit] You need a mathematical image? Ask me!

Can you draw boundaries of hyperbolic components of Mandelbrot set ? --Adam majewski (talk) 17:16, 24 January 2008 (UTC)

I don't know what is an "hyperbolic component", do you could indicate to me some information sources? Rocchini (talk) 15:56, 29 January 2008 (UTC)

I thought about something like that :

http://facstaff.unca.edu/mcmcclur/professional/CriticalBifurcationPP.pdf see page number 9

http://departments.ithaca.edu/math/docs/theses/whannahthesis.pdf see page 12--Adam majewski (talk) 19:27, 29 January 2008 (UTC)

[edit] Your images

Hey, I stumbled upon some of your graphics, and I have to say, great job! Just a quick question... what program do you use to make your images? --pbroks13^talk? 05:36, 4 April 2008 (UTC)

See Honeycomb images Color and Complex Plot Image source for reponse.

[edit] Kochanek–Bartels spline svg

You accidentally labeled 0.5 "1.5" in the Kochanek–Bartels spline illustration. I figured it would be easier for you to correct it than for me to learn how to use a vector editor. Nice illustration in any case!

Floodyberry (talk) 03:16, 27 May 2008 (UTC)

[edit] Mathematical Shapes

Hey! Got any good 11-celled Hendecatopes? PS You may like this userbox:

This User's favorite shape is E8

Wyatt 915 ? 22:05, 6 June 2008 (UTC)

Nothing better than the simplex graph since it can't exist in real space below 10-space: Tom Ruen (talk) 22:22, 6 June 2008 (UTC)

[edit] Dunce hap

I really enjoy your work, congratulations! The dunce hat animation you did is pretty good. However, it has been done two years ago, so you could perhaps build a better version with more experience and better software. Indeed, it would be nice if the animation flowed smoothly, and once all the edges are identified, the hat rotated in space to reveal more of the structure. Cheers, Randomblue (talk) 00:59, 14 June 2008 (UTC).