Darth Vader

VaderSmallI decided to try my hand at digitally illustrating Darth Vader. This was done in Photoshop with a graphic tablet in my free time over a couple of days. I am pleased with the result. As I have mentioned before, I don’t think that this type of art is one of my strong-points, however it gives great satisfaction to make an attempt and see the results.

One thing I have noticed when working on these types of things is that imperfections can make it look better. To contrast, when I work in vector art forms or cad drawings I want things as precise and perfect as possible. With this type of art, if I work really hard trying to make things perfect, I am never happy with the result. However, if I worry less about the details, the overall piece becomes much more satisfying to me.

Since we are on the theme of Darth Vader, I decided to put together a little musing I’ve been thinking about recently.

When Did Vader Learn About Luke?

There is some controversy (or at least question) over when Darth Vader discovers that Luke is the son of Anakin in Episode V. To add to the debate, there have been two different versions of the conversation with the Emperor that cloud the situation even further. After Episode 1 came out, George Lucas redid the scene with the correct actor portraying the Emperor as well as adding some new dialog. See the original dialog below.


Vader: What is thy bidding, my master?
Emperor: There is a great disturbance in the Force.
Vader: I have felt it.
Emperor: We have a new enemy — Luke Skywalker.
Vader: Yes, my master.
Emperor: He could destroy us.
Vader: He’s just a boy. Obi-Wan can no longer help him.
Emperor: The Force is strong with him. The son of Skywalker must not become a Jedi.
Vader: If he could be turned, he would become a powerful ally.
Emperor: Yes. Yes. He would be a great asset. Can it be done?
Vader: He will join us or die, my master.

I think that this dialog worked just fine for continuity’s sake. It was implied that both the Emperor and Vader acknowledged (already knew) that Luke was the son of Anakin Skywalker. They just decided to have a chat about it to decide whether he should die, or be turned.

Special Edition

Vader: What is thy bidding, my master?
Emperor: There is a great disturbance in the Force.
Vader: I have felt it.
Emperor: We have a new enemy. The young Rebel who destroyed the Death Star. I have no doubt this boy is the offspring of Anakin Skywalker.
Vader: How is that possible?
Emperor: Search your feelings, Lord Vader. You will know it to be true. He could destroy us.
Vader: He’s just a boy. Obi-Wan can no longer help him.
Emperor: The Force is strong with him. The son of Skywalker must not become a Jedi.
Vader: If he could be turned, he would become a powerful ally.
Emperor: Yes… He would be a great asset. Can it be done?
Vader: He will join us or die, master.

This new dialogue makes the situation a bit more confusing. Did Vader know of Luke’s existence? Clearly he did, as evidenced by the text from the opening crawl, “The evil lord Darth Vader, obsessed with finding young Skywalker, has dispatched thousands of remote probes into the far reaches of space….”, and this conversation with Admiral Ozzle and General Veers, “That is the system! And I am sure Skywalker is with them.”

So, we know that Darth Vader is obsessed with finding Luke, whom he at least knows by name. The revised dialogue with the Emperor implies that Vader did not know that Luke was the son of Anakin when he says, “How is that possible?”

I don’t believe that this is the case. I’m sure he knew of Luke’s lineage. Although some people see this dialogue as contradictory and bizarre, I feel that it was quite intentional, and hints at a much deeper theme of the Vader/Emperor relationship.

In Episode 3, the Emperor informs Vader that, “I’m afraid she died. … it seems in your anger, you killed her,” speaking of course of Padme. Vader then copes with the deaths of both Padme and her unborn child. I believe that those deaths became the foundation of Vader’s later actions; that he couldn’t live with himself, and truly became the evil Vader we met in, “A New Hope.”

Vader is not taken aback by the fact that Luke is the son of Anakin, but rather that the Emperor is also aware of this fact. At this point in the conversation, the Emperor basically admits to Vader of his original deceit. I believe that with this new knowledge that the path Vader has followed with the Emperor has been founded upon lies regarding the person Vader loved most, we see the beginning the redemption process that is ultimately completed in, “Return of the Jedi.”

Now that I have thought about it, I have come to like the new dialogue and the added levels of intrigue it brings to the relationship of Darth Vader and the Emperor.

No Longer Apple Computer

Apple_logo_Motter_TekturaFor the better part of my life, I could probably have been classified as an Apple “fanboy.” As a case in point, over the past few years worth of posts, a fair share of them have revolved around Apple products.

There are many reasons I have gravitated towards the Apple brand. Unsurprisingly, my first exposure to the world of computing was with my dad’s old Performa in the 80’s. Since they were my first impression of what modern computing is, I have continued to feel comfortable with, and use Apple computers. Even beyond that sentiment was the mentality of the company that resonated with me. The layout and work flow of Apple’s OS and applications just seemed so intuitive and a joy to use. Apple also had this wonderful campaign that told us that it was okay to think different, and not just blend in with the crowd.

Here’s to the crazy ones. The misfits. The rebels. The troublemakers. The round pegs in the square holes. The ones who see things differently. They’re not fond of rules. And they have no respect for the status quo. You can quote them, disagree with them, glorify or vilify them. About the only thing you can’t do is ignore them. Because they change things. They push the human race forward. And while some may see them as the crazy ones, we see genius. Because the people who are crazy enough to think they can change the world, are the ones who do.

This sentiment of rising above the status quo is something I believe we all want to achieve. That advertising campaign resonated with me, and effectively made me feel good about my choice of not using the mainstream computers of the day.

There is another quote from the early day of Apple that I also felt really explained what the computer’s role should be in our lives. The quote comes from Steve Jobs.

I remember reading an article when I was about twelve years old. I think it might have been Scientific American, where they measured the efficiency of locomotion for all these species on planet earth. How many kilocalories did they expend to get from point A to point B? And the condor won, came in at the top of the list, surpassed everything else. And humans came in about a third of the way down the list, which was not such a great showing for the crown of creation. But somebody there had the imagination to test the efficiency of a human riding a bicycle. A human riding a bicycle blew away the condor all the way off the top of the list. And it made a really big impression on me that we humans are tool builders. And that we can fashion tools that amplify these inherent abilities that we have to spectacular magnitudes. And so for me, a computer has always been a bicycle of the mind. Something that takes us far beyond our inherent abilities. And I think we’re just at the early stages of this tool.

Steve Jobs, 1990

Although quotes and advertising campaigns don’t necessarily represent a company accurately, they did create the mindset of how I perceived Apple, and how I perceived my use of computers from a very early age; that computing should be a quest for efficiency to advance the intelligence and scientific pursuits of the human kind. To not be followers, but leaders, and to have independent ideas.

Apple has always been a company I defended, loved, and depended upon. Unfortunately, Apple is no longer the same company that I grew up admiring. There has been a fundamental shift in the goals of Apple, as well as a shift in the target demographic to which Apple essays to appeal. No longer a computing company, but a device company, Apple has effectively turned their backs on many of it’s previously core-users who kept the company afloat during the hard times.

The Golden Age of Apple Computer

iMac-Bondi-Blue-1998Nearly two decades ago, Apple Computer was on the brink of death, according to… everyone. Every day, people would belittle Apple, predict their demise, etc. When Michael Dell (founder of Dell) asked what he would do with Apple if he were in Jobs’ shoes, Dell replied, “What would I do? I’d shut it down and give the money back to the shareholders.” Clearly, there was little confidence that Apple could make a recovery.

In 1997, after the return of Steve Jobs, Apple made a dramatic turn around. Steve Jobs had a knack for making computers more accessible, and less intimidating. The iMac quite literally saved Apple. Then began the golden years for Apple Computers. Each Mac World was an exciting event with fast-paced changes and innovation. OS X, G3 Towers, iBooks, Titanium Laptops. It was a wonderfully fun time to be an Apple fanatic. Finally, in 2001, the iPod was unveiled, and Apple’s course would really be changed from computer company to device company.

Fast-forward 6 years to the release of the iPhone in 2007. The iPhone was an unprecedented success. It was an innovative market disruptor (I believe those are the correct buzz-words to use here). It was probably the best thing that could have happened to Apple as a company. It naturally led to the iPad; the pinnacle of Steve Jobs’ career. His vision of a consumer electronics device that brought the power of computing literally to the fingertips of the masses. There is no doubt that the iPad is also a success. It truly felt like a magical device.

This move from computing to devices was poignantly illustrated by the simultaneous name change from Apple Computer Inc. to Apple Inc. during the original iPhone announcement in 2007.

Since then, Apple has become a device company, not a computing company.

Device Versus Computer

For me, the difference between a device and a computer is from which direction the information flows. The iPad excels at content delivery; video, social, viral, news, music, etc. It’s all so easy to navigate, experience, and enjoy from the comfort of, well, anywhere! Content creation though is more limited. Though not impossible, there are certainly far fewer tasks that can be done from an iPad than from a full desktop environment.

Computers can solve problems in the sciences (math, medicine, physics), and people can create content with so much more ease than ever before (video production, graphic arts, writing, sharing ideas). The computer was designed to make scientific and creative endeavors easier.

Apple has made it clear that they have changed their focus. That is, that they have abandoned computing in favor of mobile and fashion devices. They have found huge financial success in this focal shift, and as a company, I can’t blame them. The iPad and iPhone outsell the Mac computer line by huge factors, and represents the lion’s share of Apple’s profits. From a business perspective, they can’t be faulted. They are doing what their shareholders want; they are successful.

Unfortunately, with this success and focal shift, it also means that many of us feel that we’ve been left behind. The abandonment of the creative professionals who served as evangelists, supported the company for years, have become entrenched in the Apple ecosystem, and now don’t know what to do.

How have we been abandoned? Here are some examples from the last few years.

Applications – Professionals no longer matter

ApertureTrashApple has been “dumbing down” or in some cases completely removing professional applications. The first that comes to mind is Final Cut Pro. The change to Final Cut X was a bit of a slap in the face. Many features were removed entirely, and the whole application was made to appeal to a more consumer (or prosumer) audience. Luckily, many of the missed features have slowly been added back in, but it’s still not feature matched to what it once was.

Another application is Aperture, which isn’t being reinvented, but completely removed. Apple has even added a way to export to Adobe Lightroom, completely signalling that they don’t care about that market. And let’s face it; if a photographer is going to use Lightroom, it really doesn’t matter whether it’s from a Mac or a Windows machine.

iWork applications have also recently been redone in order to compliment the corresponding applications on the iDevices. Unfortunately the changes removed features and made some of the simpler tasks much more cumbersome. This shows to me that at Apple, the aesthetics if their applications take precedence over actually being useable and powerful.

Design – No longer a leader

Apple has traditionally led the design trends in the computer industry. So much thought is given to every Apple product. Steve Jobs was meticulous this way, and very demanding about the look and feel of a product. A computer should not be intimidating, and should be natural to use; intuitive.

Apple started many design trends over the years. Other companies often followed suit when Apple would do something bold. For example the original iMac came out, and it was so different from anything the computer world had seen. At first it was mocked, but quite soon it was emulated. Similarly, when the Titanium and Powerbook G4 came out, other companies started using aluminum and silver colors on their laptops to mimic the clean, elegant look of these Apple notebooks. Another example is the use of clean white polycarbonate plastic, like the iMac G5, iBook G4,  and MacBooks. Other manufacturer’s adopted the looks, but these were all design trends that Apple initiated.

In the realm of software, OS X was a huge departure from conventional OSes. It make heavy use of drop shadows, transparency, and color. I was enamoured by the aesthetics. It looked like the future. Eventually, these same design elements made their way to the Web and to other OSes.

Recently, It seems that rather than setting the trends, Apple has begun to follow. The new “flat” design craze was not started by Apple, and their Yosemite/iOS7 responses are completely reactionary, and quite uncharacteristic for Apple.

Flat design really goes against the original design concepts from Apple’s early days. Steve started a trend of using “skeuomorphic” design elements, or using digital analogies for every day tasks and items that people would understand, in order to make the computer less intimidating, and more intuitive. This hit it’s peak in iOS6 and Mac OS X Lion. All of a sudden, these skeuomorphic elements were erased when Scott Forstall was ousted from Apple. The new OSes have completely been redone in order to look modern by mimicking the competing OSes like Android and Windows 8.

I find that flat elements are so harder to decipher. Take a button, for example. In iOS 6, you knew a button was a button because it had an outline, and looked raised, much as you might expect a button in real life to look. Conversely, in these new flat OSes, A button might be represented by a piece of text. There is less visual differentiation of how an object behaves, which make an application harder to use intuitively. Sure, it’s useable once you know what is or isn’t a clickable element, but good interfaces shouldn’t have to be learned. They should be intuited.

Additionally, the flashy colors and transparency reduce contrast on lettering and make it more difficult to read. The thinning of font compounds this problem for some people. Apple has chosen to abandon their quest for ease of use and intuitive design in order to follow the flashy trends set by Microsoft and Google. Clearly this shows they are more interested in being a fashionable than innovative.

Hardware – Turning the back on it’s core-customer

image courtesy of iFixit

Apple has had a theme of trying to make hardware as user-friendly as possible. This extends as far back as the original Macintosh. Steve Jobs wanted the computer to just work, and to not be tampered with. Oddly, things loosened up over time, and even after Steve’s return, some of the most upgradable Macintoshes came into existence. For example, the Power Mac G3 ushered in a design that was specifically meant to allow user access to the innards and to freely add RAM, swap CPUs, replace hard drives, etc. This trend continued until quite recently.

Although the Mac Pro has done away with this to some extent, it is still provides the user with the ability to upgrade RAM and to extend the computer’s features via Thunderbolt. Still not quite like providing PCIe slots and hard drive bays, but it’s a workable solution for many people.

The most recent affront to the professional user and tinkerer is the Mac Mini. The Mac Mini has been the chosen device for many hobbyists out there due to its small price tag, upgradability, and performance. It even had the tagline, “Add memory with a twist,” for a time, referencing the bottom cover that easily twisted off to reveal user-upgradable parts. The new Mac Mini is anything but user-upgradeable. It has a metal grating with security screws where the easy access used to be. The RAM is now soldered to the motherboard, meaning that you have to anticipate in advance how much RAM you will need rather than being able to upgrade the machine over time as your needs dictate, or budget allows. And foremost, Apple has removed the build-to-order option of a quad core i7 processor.

Other machines are also seeing the user upgradability go away. The lowest-end iMac has soldered ram. No machines have socketed processors any more. This, in my opinion, decreases the life of the computers, and forces users to buy new computer more often than they would have to otherwise. Not having serviceable parts like RAM, processors, or even hard drives, makes the computers disposable. One part of the computer fails, and you have to just buy another. In short, this change shows a paradigm shift from computer company to consumables company.

Apple Watch – Finally a fashion icon

AplWatch42-34R-HomeScreen-PRINTReally? A computer company is selling a watch? A big watch? With a single-day’s worth of battery life? And they are placing the watch in fashion magazines? People really need another way to get status updates from their phones? This is just too much for me. I love my analog watch. I change the battery every couple of years. It never beeps at me or tried to grab my attention. It just sits there, always ready for me to look at it and find out what time it is.

The Bottom Line

Apple is now a fashion and device company. They no longer care about their professional users. They don’t care about their computing line anywhere near as much as they do their mobile and fashion lines.

And who can blame them?

Courtesy of MacRumors


Apple makes more money on their mobile devices in a month than they make on their computers in a year. They are making the right decisions from a business perspective. They are driving their profits up, and driving their stock prices up. There is absolutely no reason they should change what they are doing. The few people, like me, who feel disenchanted, or even betrayed, really don’t matter because there are 10 times as many teenagers who are going to buy a watch this year. We really don’t matter.

The bottom line is that the bottom line is all that matters.



Math can be beautiful. One of the mathematical things that has always intrigued me has been the visualization of the Mandelbrot set. I never tried to generate it myself until just recently. The only understanding I had previously of the Mandelbrot set was vague. I looked for some explanation on how to do the computation, but I couldn’t find an adequately succinct explanation. My brother helped me take the Mandelbrot equation and massage it into an understandable format that I could then plug into a program to generate my own image of the Mandelbrot set.

Generating the Mandelbrot set is straight forward once you understand what the Mandelbrot set really is. The fractal depicts a grid of coordinates along the x and y axis that either fall into the set or not. The formula gets computed using the x and y position for the pixel in question, and then the resulting number get put back into the equation. The resulting number either gets larger or smaller. If it passes a certain threshold, then we decide it is not a part of the set, and move on. The resulting image is a bit map of numbers that are either part of the Mandelbrot set, or not. The fun gradients and colors, with which we are all familiar, represent how many times the calculation had to be performed before the number passed the threshold.

The Mandelbrot equation is as follows, where z_(n+1) is the value for which we are solving, (z_n)² is our accumulated value so far, and C is our complex coordinate.

z_(n+1) = (z_n)² + C

We are just focusing on the right side of the equation for now, because the left contains the values that we want to solve for. Let’s expand the right side of the equation with complex coordinates so we can simplify the answer.

= (x′ + y′ × i)² + x + y × i

The next step is to expand the accumulated value. We can use our old friend FOIL.

= x′² + 2(x′ × y′ × i) + (y′ × i)² + x + y × i

The i² simplifies down to -1, reducing the number of imaginary numbers to worry about.

= x′² + 2(x′ × y′ × i) – y′² + x + y × i

Next we will move all the components with an imaginary number (i) to the right.

= (x′² + x – y′² )+( 2(x′ × y′ × i) + y × i)

Now we can the simplify by isolating the i.

= (x′² + x – y′²)+(2 × x′ × y′ + y) × i

Now the right side of the equation resembles a complex coordinate, which happens to be what we are solving for on the left.

x′′ + y′′ × i = …

So, each element of the left hand side of the equation can be solved with its counterpart element on the right.

x′′ = x′² + x – y²

y′′ = 2 × x′ × y′ + y

i = i

Since the i is equal to i, and remains independent from the rest of the variables, we can just ignore it.

Now, all we need to do is plug x and y to generate our new x′′ and y′′, and then keep plugging in the new values until the numbers go out of bounds, or we reach our threshold.

With the equation in hand, I started out by prototyping the program in Python, and outputting a Portable PixelMap (PPM) file because it is a dead-simple file format. When I first ran the program, it generated this image:


I was really disappointed that I didn’t get a meaningful image the first time I ran it. I verified the equation I was using, and the basic logic of the code, but it still came out like this. I kicked up the threshold a little bit to see what would happen, and suddenly I realized what the problem was. I was only rendering the upper left quadrant of the image. I finagled the bounds of the image, and ended up with the recognizable shape here:


This certainly looked better, but something was still off. In all the Mandelbrot images I had seen, the different threshold levels looked smooth and curved, not jagged like mine were looking. It turned out I had misunderstood how to check if the calculation was out-of-bounds. This code is the culprit:

if (abs(xT) + abs(yT)) > 10:

This is the conditional statement that decides whether the number has fallen out-of-bounds. The key is to check if the number has left the circular area that contains the entire Mandelbrot set, which has a radius of 2. This would mean that the enclosing circle is something like x′′² + y′′² = 2². The corrected out-of-bounds check looks like this:

if ((xT**2) + (yT**2)) > 4:

With that change, the images started coming out beautifully. With that, I started adding in command line options to set the bounds of the image, the depth, the gradient colors, etc. in order to easily render custom images of the set.


Now that I did it all in Python, I decided I should do it in C. Rendering 1024 pixel square image in Python takes about 15 seconds. To compare, rendering the same image in C takes .1 seconds; substantially faster!

The following code from my function, mandel(), calculates whether any given point is in the Mandelbrot set. The function takes an x and a y coordinate, and the threshold level which I call “depth”. It returns a -1 if the number is in the set, or it will return an integer representing the number of iterations it took for the point to become out-of-bounds.

int mandel(double x, double y, int depth)
    double xP=0, yP=0; // Prime Values
    double xT=0, yT=0; // Temporary Values
    int i=0;
    for (i=0; i<depth; i++)
        xT = (pow(xP, 2)) + x - (pow(yP, 2));
        yT = 2 * xP * yP + y;
        if (pow(fabs(xT),2) + pow(fabs(yT),2) > 4)
            return i;
        xP = xT;
        yP = yT;
    return -1;


The current code for both the Python and C versions are available from my GitHub page.

© 2007-2015 Michael Caldwell