Gauge Mathematical Tool

The most accurate, scalable, and consistent real-world performance benchmark for iPhone and iPod touch, and the most useful (if you’re a geek:) collection of mathematical utilities including:

        -Pi Approximator to 100 Million digits

        -Prime Number Generator

        -Mandelbrot Set fractal viewer / explorer

Available for 99 cents (USD) on the iTunes store.
Read on for screenshots and more information.

Performance Benchmarking features:

There is a large number of benchmark programs available for the PC and Mac, such as PCMark, 3DMark, Geekbench, and XBench, among many others, but there has been a dearth in this type of program’s availability for the iPhone and iPod touch. Since these two devices are very powerful hand-held computers, and both usually get upgrades at least once a year, why don’t more exist?

Gauge Mathematical Tool attempts to address this issue, providing the best all-around benchmark for the iPhone OS platform. Gauge’s benchmark intensively tests the following aspects of an Apple device:

        -CPU speed  (reflects general usage such as web page rendering time)

        -RAM  (reflects stability and smoothness when multitasking)

        -Chipset, bus, and other interconnections   (reflect general usage speed)

        -Graphics subsystem   (reflects gaming performance and fps rate)

        -SSD (solid state hard disk) read/write performance  (reflects app launch time, boot up time, and sync speed)

Because GMT’s benchmark is so well rounded, it is very reflective of speed changes that will be experienced in real world use. Many benchmarks are one-dimensional, but GMT’s is not. When a score for one iPhone OS device is 60% higher than a score for another, you can be sure that that device will be 60% faster for the average of real world use cases, which is not something competitors can state.

Gauge Mathematical Tool’s benchmark is also very useful for comparing different versions of software. Is one software version faster than another? Does jailbreaking your device slow you down? By how much? Does running processes in the background affect your iPhone or iPod touch’s stability and general performance?

Cocos Live integration:

Mathematical Utilities:

Mandelbrot Set Fractal Tools

Benoit Mandelbrot is best known for his work in fractals, infinitely complex mathematic objects, which can be just as intricately beautiful aesthetically as the math is on the inside. Mandelbrot’s lasting legacy is the Mandelbrot Set fractal, formed by the boundary of the Mandelbrot Set of numbers as drawn in the complex plane.

A true fractal, it is theoretically possible to zoom infinitely into the Mandelbrot set, but practically, computers’ ability to draw the fractal at greater zoom levels is limited by two things: their computational speed, and the precision of “double double” floating point numbers. However, it is still possible within GMT to zoom billions of times into whatever areas of the fractal you choose.

Of course, zooming this deep into the fractal would take a very long time just using GMT’s intuitive interface, so there is a manual input method, also, where an advanced user can input the coordinates of a certain area of the fractal along with a zoom amount and let GMT render the fractal from those settings without any wasted time. Users can also manually change the max number of escape iterations, and toggle anti-aliasing within this same view.

Gauge Mathematical Tool (GMT)’s Mandelbrot utilities are not just functionally useful, however. There are some really amazing images hidden within the Mandelbrot Set’s fractal.

To make things even better, GMT’s Mandelbrot Tool utilizes a unique color scheme that makes for fiery reds and oranges, and cool blues and greens, both within the same view. The contrast between these two helps to emphasize the Mandlbrot Set’s visuals.

The screen shots on the right are just the tip of the iceberg. If you have GMT, try Googling for interesting Mandelbrot Set coordinates, plug them into the Settings View, and prepare to be amazed. All this right in your pocket. But there’s more to GMT...

Pi Approximator:

Pi (3.141592...) is perhaps the world’s most famous number. It cannot be perfectly expressed in decimal form, as it’s digits go on infinitely, but powerful modern computers can approximate it to millions and billions of decimal places. Now, you can carry 10 Million digits of Pi with you in your pocket, with GMT’s Pi Tool.

In GMT’s Pi Tool, select the number of digits that you want to find. Of course, a smaller number is easier and faster for your iPhone to crunch through. 10,000 digits is a snap for any iPhone or iPod touch, and takes barely over a second on my iPod touch 3G. 10 Million is much more challenging, and may take several hours. Between those two numbers, there are many other choices. So choose a setting, and let your iDevice crunch away. When it’s finished this is what you’ll see, to the right.

Touch an individual row to view the rank of the first and last digits of a row to the right of the decimal point. Tap “Go to digit” to go to a certain digit past the right of the decimal point. Tap go to bottom or go to top to scroll to the bottom or top of the list. See the screenshots to the right for an example, or the demo video below, but the demo video does not have the automatic scrolling, as it represents an older version of GMT.

Prime Number Generator:

We all have learned what prime numbers are in grade school (A refresher: numbers that can be divided by only themselves and 1). Some mathematical savants can intuitively recite hundreds of thousands of these mystical numbers, most of us can’t. That’s where Gauge Mathematical Tool’s Prime Number Generator comes in.

Just like with the Pi tool, a user can select a number of prime numbers to find, and then view the generated list once his or her iPhone or iPod touch has finished processing the numbers. Selecting an individual prime number, similar to how the Pi tool results table works, tells you, the user, the rank of the selected prime. 2 is considered the first prime number, and 3 is considered the second (though technically, 1 qualifies as a prime number according to our definition above, it is not considered a prime number). The screen shot to the right demonstrates the Prime Number Results, and a method of scrolling to a particular prime. The second to the right demonstrates the interface common to approximating Pi or generating prime numbers.

Also of note, the pi, prime numbers, and Mandelbrot tools can also be used as individual benchmarks, using the time reported in the notification of completion of calculations as a sort of score. For serious benchmarking, use GMT’s built in full benchmark, though, as it tests many more aspects of your iPhone or iPod touch’s performance.

Video Demonstration of Gauge Mathematical Tool:

Versions 1.1 and higher of Gauge Mathematical Tool send anonymous benchmark results data to a framework called Cocos Live, which makes performance comparisons even easier than ever. Just visit GMT’s page on Cocos Live and you can see which devices get the highest scores, on average. You can also narrow the scores down into categories based on which device you want to look into more, or view only devices with a certain processor frequency or amount of RAM.

Buy in iTunes