Archive for the ‘Nova’ Tag

Daily Fractal No. 220   1 comment


Nova Mandelbrot

Nova Mandelbrot

A Mandelbrot island found in a Nova fractal. Available as a print, poster or card from Redbubble and Artflakes.

Posted 15 March 2013 by element90 in Art, Fractal

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Daily Fractal No. 207   Leave a comment


Exiled Mandelbrot No. 6

Exiled Mandelbrot No. 6

A Mandelbrot exiled from the standard set as it is found in a Nova fractal which is convergent whereas the Mandelbrot set is divergent.

Available as a print, poster or card from Redbubble and Artflakes.

Posted 2 March 2013 by element90 in Art, Fractal

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Daily Fractal No. 192   1 comment


Nova Tricorn

Nova Tricorn

The same transform that when applied to a Mandelbrot produces a Tricorn (or Mandelbar) has been applied to a Nova fractal, so where Mandelbrot islands occur Tricorns have taken their place.

Available as a print, poster or card from Redbubble and Artflakes.

Posted 15 February 2013 by element90 in Art, Fractal

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Daily Fractal No. 90   1 comment


Mandelbrot and Red Berries

Mandelbrot and Red Berries

A Mandelbrot found in a Nova fractal surrounded by patterns that give the impression of red berries. Available as a print, poster or card from Redbubble and Artflakes.

Orbit Fractals   Leave a comment


The only orbit plotted fractals (orbit fractals for short) I’ve dealt with so far are Pickover Popcorn fractals. For the next release of Saturn & Titan I decided to try plotting the orbits of a Mandelbrot instead of colouring it in the many ways that are available for escape time fractals. I modified the code that handled Pickover Popcorn to add the Orbit Mandelbrot fractal type.

This is what I got with accumulation colouring (i.e. colour based on the number of times a location is visited by an orbit):

Orbit Mandelbrot

As the fractal is essentially a Mandelbrot I considered how to add transforms to orbit fractal code, I realised that I’d modified the wrong code, the escape time fractal code already supports transforms so I added orbit plotting as an option to the escape fractals. The upshot of this is that all the escape fractals could be plotted as orbit fractals and the Pickover Popcorn fractal types are no longer required, this is because there are Pickover Popcorn escape time variants: PP Mandelbrot 4F, PP Mandelbrot 6F, PP Julia 4F & PP Julia 6F, the Pickover Popcorn 4F & Pickover Popcorn 6F fractals can be produced using PP Julia 4F & PP Julia 6F with the julia ‘seed’ value set to zero. I reduced the number of fractals types by adding function parameters and now the number is being further reduced by the introduction of the orbit plotting option.

Here are some examples of more orbit fractals:

Mandelbrots, Tricorns and Nova Circles   2 comments


In my previous post I asked what was so special about the Mandelbrot Shape. It is not just the Mandelbrot shape that turns up in other fractals, the Tricorn does as well, I suppose it isn’t that surprising as the Tricorn is related to the Mandelbrot. The Tricorn is produced by reversing the sign on the real component of the the complex number z before evaluating the same formula used for the standard Mandelbrot, the same effect is also produced by reversing the sign on the imaginary component of z instead, the images are exactly the same.

Tricorns can also appear in fractals using formula other than the modified Mandlbrot formula, an example is shown in the following gallery. When I prepared my previous post I was sure that the Mandelbrot shape also appeared when using the Sincz formula, except that I couldn’t find it, I have now and there is an explanation below the gallery.

Finally there is the case of the Nova spot, these appear quite frequently in pictures using Nova formulae and I hadn’t given them much thought. Sometimes, for example, they can obscure some detail at the centre of a spiral, it turns out that they are an artifact of the bailout condition used when producing the picture, using a smaller limit can reduce the size of the circles to a great extent and I suppose it is possible to make them so small as to virtually disappear. Personally I like them and in most cases I won’t attempt to banish them.

A gallery of mostly Mandelbrots, Tricorns, Nova Circles.

Picture 1

A Tricorn produced using the unsign real transformation assigned to the transform function,

z = transform(z)
z <- z2 + c

and calculated in the same fashion as a standard Mandelbrot, the initial value of z is set to 0.

Pictures 2, 3 & 4

A Tricorn found in a fractal using a formula other than the modified Mandelbrot form used for the Tricorn in picture 1. The formula used is,

z = transform(z)
z <- (z + z-1c2)2

the transform function is set to force the the real component of z to be negative (sign real) and again the image is calculated in the same fashion as a standard Mandelbrot. As setting z to zero would produce infinity in the second term the initial value of z is set the location (c) of the point calculated. Picture 2 shows a Mandelbrot and a Tricorn in the same image, pictures 3 and 4 show details of the Mandelbrot shape and the Tricorn from picture 2.

Pictures 5, 6 & 7

These pictures show the basic shapes of two versions of the Sincz formula differing only in the initial values assigned to z in the formula,

z <- sin(c*z)

the initial value of z can’t be 0 as would normally be the case for the standard Mandelbrot as every iteration would evaluate to zero for every point in the picture. I initially used the location (c) of the point to be calculated, no Mandelbrot shapes (picture 5), using a value of 1 on the hand changes the image completely (picture 6) and Mandelbrot shapes duly appear. The Mandelbrot shapes are clearly shown (picture 7) in the detail from the needle at the top of the image in picture 6, note picture 7 uses different colouring methods to pictures 5 and 6.

Pictures 8  & 9

For Nova fractals I usually set the bailout limit to 0.01 but for some reason (I can’t remember what) the value was set to 0.0156789 resulting in a prominent Nova circle (picture 8), changing the limit to 0.001 reduces the size considerably, but it is still there.

Posted 21 November 2011 by element90 in Fractal

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