Scientific Artist

The image of the month for May 2013 is one of the recent fractal renders.  I came across this amazing program called Incendia, written by a genius clearly, that allows you to use various fractal forms as a basis and  then you can add your own objects to the fractal.  In addition you can colour the image in ways that appeal to you and the programmer has also included a ray-tracer for added effects.  All in all a brilliant piece of software and many thanks for providing this for our entertainment.

So there’s tons of horse hair on the ground over the New Forest, and plenty hung up in the barbed wire.  But of course that’s not good enough for the resident Jackdaws – oh no – it needs to come straight from the horse if it’s to be any good.  So these 3 Jackdaws had a great time pulling great clumps of hair from this poor female grey who made no attempt to shoo them off.  I took a couple of shots of the corvid mayhem and then shooed them off myself to let her have some peace in the sunshine.

Please take the time to vote (the stars at the bottom of the page) for today’s EPOD - which is the Golden Spiral in Nature

Check out an amazing numerical asterism I found in the constellation Leo on the New Forest Observatory web site.

See plenty of new fractal renders on my Flickr Mathematical Structures page.

This image is a 42-frame micromosaic taken with the Canon 5D MkII and a research trinocular microscope at a magnification of x50.  It is the cross-section of a Curcurbits stem, an image I have done before, but not at this magnification.  The resulting 42-frame mosaic came out at 25,000 x 23,000 pixels and is the largest photomicromosaic I have assembled to date.  Well I guess Photoshop CS3 did the assembling using the Photomerge function, which also does a superb job on the blending as well.

Be warned – it took over an hour for Photoshop to put this together for me and I run a Quad core 2.5GHz Intel machine with 8 Gig of RAM and Windows 7 64-bit.  So it is not a lightweight system and yet it took this long to assemble.  Just flattening the final image took nearly half an hour!!

These massive mosaics are great fun (I wish I had enough clear skies to put together massive deep-sky mosaics – but even the mini-WASP array won’t help me out too much with that problem) – but in future I will try to stick to mosaics of about half this size, so around 20-frames.

It will not have been mentioned before in this blog, but I like certain aspects of pure mathematics as much as I like deep-sky imaging.  I think most people will have heard of the Golden-Section, or the Golden-Ratio, and how it can be obtained by dividing a straight line up into two sections one of length unity, and the other of length tau or 1.61803398…  What is less well-known is that if you wrap the line round into a circle, so the circle perimeter is divided into lengths of unity and 1.618, then then angle subtended by the unity length of the perimeter at the centre of the circle is 137.507 degrees – or the Golden Angle.

That’s where the story seems to have been left, for a very long time, but I have to wonder, why?  We started with a line (one-dimension), then moved to a circle (two-dimensions), where’s the spherical case (3-dimensions)?  I did a long search a couple of years back and couldn’t find anything on this.  So I wrote a paper on “The Golden Solid Angle” for the Mathematical Gazette, which was in fact turned down as “although the result was new, just having a new result is not necessarily having something worthy of publication” – well that’s a new one for me!  So wishing to stake my claim as the discoverer of the Golden Solid Angle (sent to the Mathematical Gazette on Thursday 14th June 2007) here’s the thing explained for the first time below.

Divide the surface of a sphere into two regions, one of surface area unity, and the other of surface area 1.618…  The surface area of unity will subtend a solid angle gamma at the centre of the sphere.  By noting the total solid angle about a point is 4Pi Steradians, we can derive the following equation for gamma:

(4Pi – gamma)/gamma = 4Pi/(4Pi – gamma)

Giving a quadratic in gamma which can be solved in the usual way to give:

gamma = 1.52786Pi Steradians or 15757.2 square degrees.

Question is, does anyone out there know where the Golden Solid Angle, gamma, makes an appearance in the Natural world (or basically, anywhere)?  If you do then please let me know ASAP

Since writing the above I have found that using Phi to represent the Golden Ratio we have:

Golden Angle = 2 Pi / Phi squared

Golden Solid Angle = 4 Pi / Phi squared

Nice!!

Simple – but I really like this one

I will put most of my fractal renders on Flickr and will now only post the most impressive here.

Two more fractal renders from the amazing Incendia software.