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Where photography and mathematics intersect with some photography, some math, some math of photography, and an occasional tutorial.

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Saturday, July 16, 2011

Moore's Law and Digital Photography

Kenneth Osborn
Misterken Photography
© July 17, 2011

“The complexity for minimum component costs has increased at a rate of roughly a factor of two per year... Certainly over the short term this rate can be expected to continue, if not to increase.”

I entered the digital domain of photography in 2001 with a point and shoot Olympus 3000 that had an incredible resolution of 3 mega-pixals!  I was using a MAC cube computer with 20 Giga-bytes (GB) of storage, seemingly massive quantities of capacity that would surely serve me for a long time.  Compared to text files, image files seemed large at 600 Kilo-bytes (KB), but 20 GB could hold over 30,000 images from my Olympus, enough for years to come! 

And then came the digital revolution with new cameras capable of resolutions approaching and exceeding the 35 mm format of the nearly forgotten days of film and wet chemistry.  Now image file sizes of 20-30 MB are common and digital imaging chips in cameras are capable of holding several GB of images.  Even one Tera-byte (TB) drives seem inadequate.  My personal collection numbers 123,000 stored images filling some 600 GB of storage and that does not include backups.  Will Moore’s Law get us through the next decade?  Will we be able to afford to continue our passion for digital photography as the technology makes today’s cameras as obsolete as today’s cameras outshine those of a decade ago?  

So with a database of 123,000 images spread amongst 973 master folders, how does the growth of this one photographer’s obsession compare to the projected growth of storage capabilities if Moore’s Law applies? 

Collecting the data into a useable format that could be analyzed in Excel ® or a statistical package was not straight forward.  However, a small readily written program was run in Apple’s command line interface (CLI) to collect file sizes, designations, and file dates and write the results to a text file that could be parsed and analyzed in Excel ®. 

To understand how differing growth rates may positively or negatively affect the future of digital photography, it is helpful to take a look at the mathematics of growth.  Growth in any system, whether it is digital image files, your bank account, trees in a forest, books in your library, or weeds in your garden can be simple or compound.  Systems of simple growth seem to be limited to things like shelves for your books, freeways, and the plants you want to cultivate while compound growth seems to be a property of weeds, your growing collection of books, and cars on the freeway.   

Chart #1 is an example comparing simple versus compound growth for $1000 placed in an interest bearing account paying 10% per year.  The red bars represent what happens when the interest is compounded and the blue bars represent simple growth.  I need not elaborate which is the better investment.  

Chart I: Compound versus simple growth of $1000 invested at 10%

Storage needs (yours) and storage capacity (Moore’s Law) follow a compound growth curve. An interesting thing about compound growth is how it seems to accelerate with time.  Looking at Chart I, note that for the first few years there is little difference between compound and simple growth.  If the growth rate is increased, the acceleration becomes even more obvious as in Chart II. 

Chart II: Comparison of two rates of compound growth

When there is a large difference between two rates of compound growth, there is a rapid separation.  Like a rapidly growing need for storage versus a slower growing storage capacity. 

Chart III shows the growth in my photography over the period from 2001 to mid-2011.  The green line plots the number of photographic events (as folders) per year and the blue line plots the average folder size for each year.  When the events are combined with the average folder sizes, the results in Chart IV show the growth of file space requirements.  

Chart III: Annual growth in number of photographic events (as folders) and average folder size from the period 2001 to mid-2011

Chart IV: Annual growth in image storage requirements in GB

The question remains: has the growth rate of my image file requirements exceeded the growth rate for future storage capacity as predicted by Moore’s Law.  Chart V is Moore’s Law plotted on log chart paper.

Chart V: Moore’s Law of capacity versus year plotted on a logarithmic scale

A logarithmic transformation of the data in Chart IV provides Chart VI, showing a similarity to Moore’s law rate of growth.  The data are plotted in blue and a linear trend line is plotted in black.  So how does the slope of the trend line in Chart VI compare to the fitted curve in Chart V for Moore’s Law? 

Chart VI: Logarithmic transformation of annualized growth in folder sizes for my photos

Note that while the units in Charts V and VI appear to be different, 0.001 to 1000 for Chart V and 0 to 3 for Chart VI, since the logarithm of 1000 = 3, log 100 = 2, etc, the units are conformable.  If the scales of the two charts are made to conform on the Y-axis, then the two straight lines can be compared directly.  This is performed by physically scaling the log-transform chart to match the 3 with the 1000 on Moore’s Law plot and the 0 with 1.  The log-transform plot is then moved laterally until the two straight lines are close, but sufficiently separated to determine if one has a steeper angle than the other.  If Moore’s Law will be exceeded, then the linear trend line for my folder growth will have a steeper angle.   Chart VII answers that question.  The green dots are the data for the Moore’s Law plot, the blue connected dots are the logarithmic transformed digital photography data, and the straight lines of the two plots are parallel and neither growth rate exceeds the other. 

Chart VII: Comparison of Moore’s Law plot versus digital photos storage growth by direct superimposition and scaling of charts V and VI. 

My conclusion is that storage capacity will provide my storage requirement needs for the near future.  Of course, I’m now starting to experiment with video…. 

1)    Moore, Gordon E. (1965). "Cramming more components onto integrated circuits"

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