We're glad to share again one of our favorite parametric images, first appearing on Handshake 2.0 in April of 2009:  an egg-colored ellipsoid, with three parametric sine functions wrapping around it at various points.

For the math behind Handshake 2.0's Parametric Egg, feel free to read this .pdf.

Alex Edelman is the author of Parametric Hand Turkey, Parametric Valentine, Parametric Shamrock and Handshake 2.0's parametric images, all created using Mathematica.   Alex Edelman's parametric creations have been listed on Wolfram Research News & Events.

The original Parametric Tree was created using Wolfram's Mathematica by Alex Edelman and appeared on Handshake 2.0 last year.  This year, Kelsey Sarles of Coldwell Banker Townside, REALTORS(R), decorated it for the holidays!

Seasons greetings and best wishes for a wonderful 2011 from from Coldwell Banker Townside, REALTORS and Handshake 2.0!

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You're invited to view all the parametric images on Handshake 2.0.

Coldwell Banker Townside, REALTORS (R), is a full service real estate agency specializing in Blacksburg, Christiansburg, Roanoke, and Salem, Virginia real estate and homes.  You're invited to learn all about the Coldwell Banker Townside App, check out the CBTownside blog, Keepin' It Real Estate, visit Coldwell Banker Townside, REALTORS (R) on Facebook, follow Coldwell Banker Townside on Twitter, and learn more about Coldwell Banker Townside on Handshake 2.0. 

Coldwell Banker Townside, REALTORS (R) is a client of Handshake Media, Incorporated, the parent company of Handshake 2.0.

From Alex Edelman:

This year's parametric holiday present comes wrapped in Mathematica's Cuboid and Line graphics primitives. The bow is the more interesting Lorenz attractor, a particularly neat-looking solution to the differential equations governing the Lorenz oscillator. You can download the Mathematica notebook that generated this image here. (If you don't have Mathematica, Mathematica Player should let you see what's going on.)

The Parametric Present was created using Wolfram's Mathematica by Alex Edelman. You're invited to view all the parametric images on Handshake 2.0.

This classic post from Alex Edelman originally appeared on Handshake 2.0 in 2008.

The quintessential childhood Thanksgiving arts-and-crafts project is the hand turkey, so I decided to make one. Unfortunately, a rigorous scientific education has enabled me to suck all the fun and child-like innocence out of any enterprise, so I ended up making a graph.

The graph in question is of a parametric equation. Whereas the graphs we are most familiar with give one variable as a function of another (y in terms of x, for instance), a parametric graph gives x and y in terms of another, or in our case, two other variables. I've parameterized in terms of r and t.

 

 

 

 

The parameterization, in terms of t, graphs the "shape" or "outline" of our mathematical hand turkey. It's a modification of a polar function that would normally give us a "rose" with nine petals. My fingers are not all the same size, though, so I tweaked the function with a square root of t to vary the petals a little bit. A few more changes gave me five "fingers."

 

Then, I multiplied by my second parameter, r. Since it ranges from 0 to 1, then for every possible value of r, the "t" function it is affecting will be drawn with a slightly different radius. When we put all these functions on top of each other, we get a continuous series of "outlines" which smoothly merge into a solid region.

Not entirely devoid of childlike aesthetic taste, I then used Mathematica to graph the function and, more importantly, apply a gradient of "Thanksgiving colors" to it.

All in all, though, you're still probably better off asking your kid to make a hand turkey.

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If you're interested here's a high-resolution .pdf of the Mathematica notebook. It's big (8559K), and requires a little crunching from your computer, but the image it produces is gorgeous.

And for the sake of complete documentation, here's the original Mathematica notebook, in case readers of Handshake 2.0 use Mathematica.

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The Parametric New Year's Horn image was created using Wolfram's Mathematica by Alex Edelman. You're invited to view all the parametric images on Handshake 2.0.

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The Parametric Tree image was created using Wolfram's Mathematica by Alex Edelman. You're invited to view all the parametric images on Handshake 2.0.

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The Parametric Pumpkin Pie image was created using Wolfram's Mathematica by Alex Edelman. Here's a high-resolution .pdf of the Mathematica Notebook.  Here are all the parametric images on Handshake 2.0.

Media fragmentation scatters the marketplace like a bag of marbles spilled on a kitchen floor.  Target market groups disperse.  Some settle into niches, some skitter into unreachable places, and some continue to roll into the unknown.

In an age of media fragmentation, reaching target market “marbles” takes time.  In an age of social media, target market “marbles” have to be invited back into the bag.  That, too, takes time.

Time costs money.  To cut costs, how can companies automate the target market marble-collection process?

In some ways, the sales funnel automates it for us.

According to the sales funnel theory, while many prospects may fill the large opening at the top of the funnel of the conversion-to-sales process, only a few reach the narrow opening at the end of the process and become customers by buying a product or service.

When I go to a business networking meeting, let’s say with 100 people present, I may be able to shake hands with 10.  If my handshake-to-conversion ratio is 10 to 1, from that business meeting, I may get one new client.  The sales funnel allows only the few to emerge from the many.

According to Wikipedia, a quarter of the world’s population has Internet access.  A quarter of 6 billion people is 1.5 billion people.

When I add a post to a blog, or an update to Twitter, or a video to YouTube - offer new information online in some way - I reach out a virtual handshake to a potential 1.5 billion people.  With a 10 to 1 handshake-to-conversion ratio, I may get 150 million new clients.

Offline, I may meet 100, but online I may meet 150 million, simply by offering new and useful information?

Dozens of factors limit this simple metaphor and simplistic example and make the numbers inaccurate.

But the concept is sound.  Offline I connect with the few and online I connect with the many? 

That’s a lot of marbles entering the sales funnel.

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Parametric Social Media Sales Funnel image created using Wolfram's Mathematica by Alex Edelman.  If you're interested, here's a high-resolution .pdf of the Mathematica Notebook.

From Anne Clelland:

Handshake 2.0 predicts how a regional social media initiative would look - every regional business using social media - blogging, using Twitter, Facebook, LinkedIn and more - to connect with each other and others outside the region.  The peak at the center of the image represents the "It's who you know" power of a connected business region. 

The points not at the peak represent everyone else.

A Regional Social Media Initiative:
The Handshake 2.0 Effect  

That's how a regional social media initiative would look.  How would it work?  First, it's about quantity.  Every regional blog post, every Tweet, every LinkedIn update is another small stone added to the growing mountain of a region's presence in the global realm of the Internet.

Second, it's about sharing regional riches.  According to Daryl Scott, President and CEO of Attaain, Inc., from a blog post on Inside VT KnowledgeWorks, "When a highly ranked site or blog links to you, it is in essence 'sharing its reputation' with your site, and therefore drives up the reputation of your own site."  The more a region's businesses connect online with each other, the more accumulated value a region brings to itself.

Most importantly, it's about quality.  In that same post, Daryl Scott points out, "The implication [however] is that getting links from low ranked/'poor reputation' sites doesn't really help you - something that people often overlook in the quest to get links into their sites."  To really be part of the growth and development of a region, each business has to offer the greatest quality it can generate.

Ultimately, it's about excellence.  Sure, social media tools are new, but their call to excellence is not.  Sharing information about missions, visions, leadership, outstanding products and services with their customers and clients?  Connecting with their fellow businesses?  Being part of initiatives that benefit an entire community, even region, even the world?

That's what great businesses already do.

And that's what great leaders already do.

Whether the medium of communication is sign language, the telegraph, Web 2.0, or Web 200.0, a region's visionary leaders lead. 

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Regional initiatives can have "who" and "where" challenges.  The New River Valley and Roanoke Valley regions of Virginia are sometimes termed "NewVa" as opposed to "NoVa" in Northern Virginia, "RNR" for the Roanoke and New River Valleys, and the "I-81 Corridor" for the region's access to Interstate 81.

Regardless of what the region is called, great businesses with great leaders are in place, and resources exist, to consciously create a regional social media initiative of quantity, riches, quality, and excellence as a means of, right here, right now, taking action on regional economic development.

Regionalism advocate Stuart Mease describes a regional divide between those who exclusively connect online and those who exclusively connect offline.  An extended dialogue on this view of a regional divide occurred via blog post comments.  He offers suggestions for how to bridge the regional online-offline divide using a mix of both traditional and social media to connect businesses in a region.

Handshake 2.0 offers a vision of every regional business blogging as part of an online business strategy and describes the value of a single blog post.  We address the evolving nature of online PR and marketing, and describe our own business model and founding as part of a regional economic initiative.

An egg-colored ellipsoid, with three parametric sine functions wrapping around it at various points.

For the math behind Handshake 2.0's Parametric Egg, feel free to read this .pdf.

Handshake 2.0's Web 2.0 developer is the author of Parametric Hand Turkey, Parametric Valentine, and Parametric Shamrock, all created using Mathematica.   Handshake 2.0's Web 2.0 developer's parametric creations have been listed on Wolfram Research News & Events.