Mathematica 10 Keygen Osx Snow
Rene Thivierge
Physics-based answers are to be preferred, but graphics only solutions are also welcome.There already is a thread on generating a snowfall, here: How to create animated snowfall? and one of the posts addresses the problem of generating snowflake-like elements.In the snowfall post, though, emphasis is on efficient generation of 'snowlike' ensembles. The purpose of this question (apart from having some 'seasonal' fun) is to create graphics that details the structure of a single snowflake. Efficiency is not the primary issue here: beauty is. A very detailed snowflake rendering could even take several minutes of computer power, thus making it unsuitable to incorporate into a snowfall simulation.
Here we are trying to generate a single snowflake (possibly with different parameters to tune its shape), the more realistic, the better.Three dimensional renderings, for adding translucency and colors are also welcome. Unleash your fantasy, go beyond the usual fractals!
And if your fantasy is momentarily faltering, as Silvia pointed out in a comment below, on this website you can find a lot of information - and even a C program for the Gravner-Griffeath 2D Snowfake Simulator - on how to generate 'virtual snowflakes', even in 3D (have a look at the pdf files: "Modeling Snow Crystal Growth" I, II and III).
Those 26 probabilities, pFreeze and pMelt, can be determined by some serious physical models, or can be chosen randomly just for fun. Then they can be used to establish rule function for CellularAutomaton:
So I decided to write an app to imitate the process. It also can be used to make random snowflakes (similar to to @bill s' but with reflection to imitate real cutting paper process and reflective symmetry of snowflakes). App and random collection are below.
@Silvia did a beautiful job, especially at design and explanation. I still want to point out similar things with Cellular Automata (for the sake of a bit alternative implementation) and a bit different things in general.
Not so much snowflakes as random artworks with the same symmetry as snowflakes, but I wanted to join in the festive fun! These are generated with a "randomart" package I wrote a while ago (code at the bottom of the answer). It uses a kind of non-linear iterated function system to generate random images.
It's a simple 3D cross fractal (this code is a reduced version of this monster). Although it's 3D, you get 2D figures. In this case Koch outlines. I wonder what kinds of 2D hex systems you could describe in terms of 3D, and vice-versa (e.g. an automaton rule on a 3D grid which is perspectivally equivalent to an automaton rule on a hex lattice).
I work on geometric computation and graphics in Mathematica, and for Mathematica 6 I was responsible for our new surface-drawing capabilities. When I talk about my work at university mathematics departments, I am often told that I just have to see what the department has tucked away in some corner of its building: plaster casts of intriguing mathematical surfaces, created in the early part of the twentieth century to illustrate the achievements of the field of differential geometry.
For more than a century it had been believed that the minimal-area surfaces made by things like soap films had to follow a small number of possible forms. But in the 1980s it was discovered that another form, known as the Costa surface, was also possible. A few years after Mathematica was released, pioneering Mathematica user Alfred Gray managed to find a way to construct the Costa surface just using ParametricPlot3D, together with the function WeierstrassP.
After reviewing the Mathematica documentation and completing the Signal Processing course, I am having difficulty in visualizing both transverse waves and standing waves using the Mathematica functions Manipulate[] and Sin[]. Please review the attached notebook and advise me as to what I am missing either in the coding or my understanding.
Thanks,
Mitch Sandlin
Whenever I use your snippet of a standing wave as you supplied Manipulating the "t" slider seems to superimpose the two wavelengths as expected. However, when Lambda (wavelength), f(frequency) and b (phase angle are added in as sliders, only Lambda and b seem to have any effect on the wavelength. See below.
This is exactly what happened to the transverse wave, that I initially supplied, except with the f (frequency) and t (time) sliders not working correctly. The examples that I listed in my inquiry are the standard mathematical representations of: simple harmonic motion, the transverse wave and a standing wave so it seems the formulas should work in Mathematica. Currently, I am still trying to understand how to plot the transverse wave and standing wave and having all the sliders work correctly.
I guess I now see your problem: When you move the frequency slider you see just a phase shift. But frequency has to do with time: depending your frequency adjustment if you move the time slider you will notice the difference.
I do know that all of the Mathematica documentation is written in
Mathematica itself. But nowhere in this documentation do I see how to
enter ordinary text or chapter titles in a Mathematica notebook.I have an MSc degree and teach in the Danish 3-year Sixth Form College
for the 16-19-year-olds. After the summer vacation next year I am to
take an extra BSc degree in Physics and Astronomy and this is where I
will need the ability to write reports in Mathematica, including text,
formulas and graphics.So I am even considering to wait with the purchase of a new Mathematica
- after all the I've got version 5 from 2003, the present version is 7
and version 8 might have come then.And - I don't even see anything particularly about the issue in Stephen
Wolfram's "The Mathematica Book 5th Edition". With 1,500 pages. Only a
few hints.
--
Per Erik R=F8nne
Errare humanum est, sed in errore perseverare turpe
I never used "teacher edition" of Mathematica. It does not allow you to
select a different styles and ability to insert text cells?On standard Mathematica, you can use a style sheet such as report or book,
change the cell style to title, then you can add a text cell to enter text.If it will help, here is a small movie just made to show you, AVI file, in
this folder (12 MB) _cell_5_8_2010/hth--Nasser
This can be approached at different levels.First, I'm not familiar with the capabilities and pricing of the various
versions of Mathematica but, if you can manage it and plan to do a lot of
technical work, get up to date with the latest version and keep up to date.
There is a world of difference between Version 7 and Version 5. The dynamics
and improved graphics extend the ability to communicate by an order of
magnitude - or more.At the present time, the single most serious problem with writing reports
and books in Mathematica is that people who do not have Mathematica can't
easily read them. There is PlayerPro but that cost about $200 and few people
will pay that just to read your paper or report. The free Player is a
partial solution but it is very restricted. You have to send it through some
process at WRI, you can't use an independent package with it, and you can't
write custom dynamics but are restricted to the single Manipulate statement.
I'm hoping that WRI will come up with a better solution to this, something
like the free Acrobat reader. We'll have to wait and see. You can "print" a
notebook as a PDF but that loses all the dynamics.Other than that, Mathematica offers capabilities as a technical development
and communication medium that are far beyond present practice with static
media. I would even consider it as a new field, ripe for development. We
have a lot to learn on how to use the new capabilities Mathematica gives us.
You can easily add titles, subtitles, sections, subsections and text cells
to your notebooks. Each of these is a cell style. These are defined in the
various style sheets that Mathematica uses for the notebooks - for example,
the Default style sheet. I forget on which Menu item it occurs in Version 5,
but there is a Show Toolbar option that will add a toolbar at the top of
your notebook. It has a drop-down menu for starting various cell types. You
can also use Menu, Format, Style to see the various cell styles, and this
listing also gives the shortcut keys for those styles that have them.Many users use Mathematica simply as a "programmable super graphical
calculator", without any sectional structure, but my opinion is that it is
much better to write notebooks as literate documents with structure and
plenty of textual explanation.At a higher level you can use Workbench in conjunction with Mathematica to
write Applications that might contain a book, ancillary packages, and
documentation that ties it all together. Once you get it set up, you can do
most of your mathematical development and writing in the regular Mathematica
environment and only go to Workbench when you want to put material into a
"finished" form. This is a very good way to organize and preserve your work
in an active usable form, and to present it to other Mathematica users.Roger Williams has done two YouTube videos on Mathematica as the latest
medium for technical communication. He traces over three millennia of
technical communication and illustrates all the advantages of the active,
dynamic medium that Mathematica is. (He had posted a version of this on
MathGroup earlier, but this is a new and much improved version.) ==-b0B5hp0hAQ ==Pm6yrevYcjQ
David Park
djm...@comcast.net
djmpark/
I am the not quote happy owner of Mathematica Teacher's Edition [it
doesn't work on Snow Leopard] and I do now see a future need to write
reports / books using Mathematica - though of course I would then have
for the 16-19-year-olds. After the summer vacation next year I am to
take an extra BSc degree in Physics and Astronomy and this is where I
will need the ability to write reports in Mathematica, including text,
formulas and graphics.