OPTi Home Page

Last update: 2016.5.17

icon What is OPTi ?

"OPTi" is a Macintosh application program which visualizes quasi-conformal deformations of the once-punctured-torus groups. It interactively draws the isometric circles, the Ford region, the limit set, etc.

OPTi screen
Click for a large picture

icon What's new ?

OPTi 4.0.2 fixes a bug where OPTi did not show windows properly under Mac OS X 10.9.

OPTi 4.0 released. Download OPTi 4.0 from the Mac App Store. OPTi 4.0 runs under Mac OS X 10.9 and later. (2016.5.18)

Corrected the link to OPTi 3.61. (2011.6.7)

There is nothing really new, but I have packaged OPTi 3.61 with 3.60 documents in zip format, rather than sit format. 2010.12.4.

Source files now available for further modification 2006.4.22

Now I provide the source codes of OPTi for those who are interested in the inner workings of OPTi. Modification of the program is welcomed.

Also, there has been a request for my old program called "CyclicGroup", and I am making it together with its source codes available for download.

Documents available for OPTi 2002.10.30

I have uploaded a few of my preprints related to OPTi. See below in the download section.

OPTi 3.60 (20020909)

OPTi goes 3D!! Now OPTi shows the Ford region of a given group in a realistic 3D view. Just choose "Show 3D View" from the "Group" menu. The OpenGL graphics library, which is needed in order to use the menu, is included in Mac OS X as well as in recent versions of Mac OS 9. But if you are using older versions of Mac OS, you may need to download and install appropriate versions of CarbonLib and/or OpenGLLibrary from the Apple website.

Also OPTi 3.60 now uses more feasible colors for the parameter space of the Maskit slice. The randomly looking colors shown in the Maskit's parameter space by OPTi 3.50 were due to numerical errors. Cusps are very unstable in the sense that infinitely many groups having different Ford region types reside near each cusp. Thus a very small numerical error could cause a group to look having a totally different Ford region from the original. Therefore, the pictures of Maskit slice obtained by OPTi 3.50 and by OPTi 3.60 are both correct in the mathematical sense, but of course we prefer the latter.

Server Down 2002.10.1

Our server has been down for about 3 weeks because of a malicious act of an intruder. I am sorry for any inconvenience caused by this. Now the site is up again, and I will soon post a new version of OPTi.

Revision History

icon Download

OPTi 3.61 --- OPTi 3.60 User's Manual, and some sample files are archived as a zip file. The program runs under Mac OS X (using Rosetta for Intel Macs) as well as Mac OS 9.

OPTi 3.61 source files --- CodeWarrior Pro 8.3 project and source files, archived in zip format. Modification of the program is welcomed, if anybody is interested.

"OPTi 3.60" program, OPTi User's Manual, and some sample files are archived as a BinHexed StuffIt file. The program runs under Mac OS X as well as Mac OS 9.

You will need "StuffIt Expander" (freeware) to expand the downloaded file.

OPTi 3.60 --- runs on Mac OS X as well as Mac OS 9. (357KB)

OPTi 3.50 --- runs on Mac OS X as well as Mac OS 9. (308KB)

If you use Mac OS 8 or older, you may need to use an older version of OPTi:

OPTi 3.30 --- runs on PPC macs only. (461KB)

OPTi 3.21 --- runs on both PPC and 68K macs. (771KB)

CyclicGroup --- Classic application, and its source files.

Here are some documents about OPTi in PDF format.


"OPTi 3.60" is a freeware program. You may freely copy and distribute "OPTi 3.60".

If you use pictures produced by this program for your publication, I would appreciate it very much if you send me a copy of the pulication (whole or part) containing the picture, or at least tell me where I can find it.

Bug report

Every program of this complexity contains a bug or two. If you find any, please report it by sending email to wada@ist.osaka-u.ac.jp. It would greatly help me improve the program.

Go to Home of Masaaki Wada