When you own a terrier (or two), it often seems like ten canine cyclones are competing for your attention. This is our Westie (West Highland Terrier) Katy, lounging about in a rare moment of calm.

Well, of course, it's actually TEN Katys (look carefully) in a Photoshop composite I created a few years ago. The process is actually quite simple, but requires careful preparation for best results.

The camera was secured on a tripod and set to manual focus and exposure, then multiple photos were taken (lit by 2 remote strobes) with Katy placed in a different position for each shot.

The images were then layered in Photoshop and in all but the bottom layer each Katy was clipped out and the background removed. Judicious selection, exact registration, and proper feathering around each layer makes it virtually impossible to detect which is the "actual" original shot with only one terrier present, even in the final 13" x 19" print.

The trickiest part of the process is getting a natural look where parts of one Katy overlay another. Oh, getting the model to cooperate and sit still was also a bit tricky

After 20 years of foot and paw traffic, our dining room floor was looking shabby. The original teak parquet had accumulated countless scratches and water stains, and faded to a dull lifeless color.

Replacing the floor would be too expensive (and teak hardwood parquet is no longer available), so I considered refinishing the wood.

Unfortunately, consulting the manufacturer's original product literature was discouraging - "Never sand or refinish the parquet tiles", it admonished.

Not one to blindly follow instructions, I figured I had nothing to lose and grabbed a belt sander, carefully grinding away the topmost layers of wax, stains, and scratches. (Using a floor or drum sander would have likely destroyed the pieced tiles.)

A few days of sanding, re-staining, and 2 coats of polyurethane did the trick. Sometimes it pays to forge ahead and ignore those words of advice from the experts.

Hopefully, we'll get another 20 years of use!

My wife and I first met Jim Warren and saw his paintings at the Westwood Art Show in 1985. We instantly fell in love with his art, beautifully detailed yet surreal scenes that draw the viewer in for a closer look.

In that same year, Jim began creating book and album covers, popular movie posters, and magazine covers, garnering an ever-growing number of admirers.

In 1990 his work "Earth...Love it or Lose it" received critical acclaim and became a symbol for the emerging global environmental movement. In 1992 he collaborated with famed marine life artist Wyland, producing a series of works showcasing their combined talents.

Jim Warren published two books, The art of Jim Warren: An American Original and Painted Worlds, and in 2004 began a series of Disney/Warren fine art prints featuring popular Disney characters. He continues to paint imaginative and fanciful scenes, many of which are available as limited edition prints.

Visit his website jimwarren.com and spend some time viewing his colorful gallery of paintings.

In any primer on Number Theory, a primary factor is the study of prime numbers. (Sorry, I couldn't resist that, um, pun-filled line.)

There are many interesting relationships that arise from the properties of primes (an integer divisible only by 1 and itself). Just for fun, I'll be posting occasional factoids involving primes or basic number theory. Even if you're not a math geek, I promise your head won't explode.

First up: Sphenic Numbers


A sphenic number is an integer that results from multiplying 3 distinct primes. For example, the first sphenic number is 30, which you get by multiplying the primes 2, 3, and 5.

     n = p₁ * p₂ * p₃   where p_n are primes
     30 = 2 * 3 * 5

The first 10 sphenic numbers are 30, 42, 66, 70, 78, 102, 105, 110, 114, and 130. Note that 105 is the very first odd sphenic number and shares a few other notable properties.

Every sphenic number has exactly 8 divisors, no more and no less. For 30, the divisors are {1, 2, 3, 5, 6, 10, 15, 30}; for 42 we get {1, 2, 3, 6, 7, 14, 21, 42}. While this might seem unusual at first glance, it's easy to demonstrate. Remember that every sphenic number is the product of 3 primes:

      n = p * q * r

Since no prime has any factor other than itself (and 1), the only possible divisors of the result are:

     {1, p, q, r, p*q, p*r, q*r, n}

Exercise: With any product of 4 unique primes, how many possible divisors will there be?
(Answer: Mouse over the image "105" in this blog)

Today I was revising some web pages on my primary website mvoDesign and decided to design a background similar to that which adorns these pages.

I chose another photo from my portfolio of waterdrop macro images, which captures a small droplet just as it plunges into a clear glass of water. Three studio strobes froze the motion, and colored gels tinted the waterdrop with a saturated red color.

In the slightly revised version above, I changed the overall hue in Photoshop to get an ice blue color, which actually looks more natural than the un-retouched red version, which you can see here. I love the "fractured" look within the droplet, which probably results from internal light reflections of the drop/water interface at the plane of impact.

To see more of these photos, feel free to visit my water art gallery. The two studio sessions I did back in early 2007 were a great learning experience which tested my patience (something I sorely lack), but yielded some wonderful images that I continue to enjoy today.

For the technically curious, a photo and detailed description of the camera setup appears on PixArtWeb in a blog entry I made in September 2008.

Gary Larson could tell a story (and a funny one at that) with a cleverly drawn sketch in a box. Poets and novelists beguile or captivate us with a mere string of words. And now the web gives everyone a platform on which to speak their minds in countless public discussion boards and blogs, littering the literary landscape with meager meanderings (and absurd alliteration).

So here, grudgingly, I present another personal blog destined to inflict further damage on social progress. I haven't the merest whit of Larson's clever whimsy or Tennyson's poetic flair, but I'll do my best to avoid embarrassment and write only of things about which I have no useful or penetrating insight.

I'll begin with a bit of background. My first name is Daryl, but early on I learned to favor my middle name Mark since none of my grammar school teachers (stern Irish nuns) could pronounce Daryl in a way that didn't sound distinctly feminine. My last name is Dutch, but the lineage includes some German and Austrian for good Teutonic measure. Not much of that survived the 3 generations since my ancestors emigrated, so I'm thoroughly American for better or worse.

I grew up in the tumultuous 1960's and 70's, so I have a strong sense of both the power and failures of people and their governments. I'm not a musician, but have a great love for music - what child of the 60's wouldn't? I grew up in a Catholic household, but abandoned the strident dogma as soon as rational thought kicked in.

Perhaps most crucially, I was influenced early in life to pursue scientific inquiry by my father, a metallurgical engineer who was quiet and strict, but well possessed of a dry wit and boundless curiosity. He was proud, yet often dismayed, that the curiosity passed on to me was all too often evidenced by disassembly of anything mechanical or electronic that I happened to find. I was one of those tinkerers who always found a greater joy in probing the inner workings of a device than in its actual purported use. Which is to say, many of those innocent items either came to an untimely end or a novel re-purpose.

My early education was uneventful as I followed the wisdom of the Japanese saying, "Deru kugi wa utareru" (The nail that sticks up will be hammered down). That worked for awhile, until routine intelligence tests in middle school betrayed me to my parents and teachers.

Sudden enrollment in "gifted" student programs and parental demands for higher grades dampened my enthusiasm for focusing attention on everything BUT whatever the teacher was blathering on about. Fortunately, a wise teacher in 8th grade sparked my interest in mathematics and I found something that actually had educational merit with which I could distract myself during boring classes.

It wasn't until college that I started earning those expected grades while taking courses in math and physics. I found that solving problems was immensely rewarding. Better yet, my notoriously poor memory for facts, dates, and names - something that haunted me throughout elementary school - was now of little consequence since I could analytically derive a needed equation from basic principles instead of memorizing the damn thing.

Such kismet, then, that personal computers became mainstream just as I graduated college. I had delved into logic and binary algebra during high school, but now the computer revolution was here. My love for physics, while undiminished, was deflected toward microprocessors and software development. I had finally found a vocation that merged so many of my favorite things: math, logic, language, and tinkering.

And best of all, I could make computers do my bidding ... yeah, baby!