UltraIterator

NegPhoenix Sharp Spirals

2012-01-27T19:42:00.001+10:30

A while back I noticed that the regular Phoenix formula can be made to behave similarly to the (generalized) Mandelbrot. If you use an exponent with a negative non-integer real value, areas can be found containing reasonably dense, space-filling detail. The quality of the detail is similar to negMandel too - an intense amount of branch-cuts overlaid and interfering with each other in an interesting way. There does seem to be a subtle difference in the themes of texture that you find there too.

Starting off I revisited this area that has these nice spiky spiral shapes in it:

I went on some forays away from this area, in search of other interesting textures, wouldn't say I was particularly successful with that to begin with, but some nice things came of it in the end:

I was quite pleased with this thread of gold/blue crystal fibers:

This last one has a nice kind of Blade Runner-esque feeling to it:

Coil Upon Coil

2011-12-10T17:09:00.002+10:30

Today I've got a selection of recent phoenixDoubleNovas, This initial burst makes an interesting progression to some of the later places.

Apologies for the spew-coloring at this juncture:

Ok, it's a bit ugly, but at least some good came of it in the end:

Negmandel Fibers and Light

2011-11-14T12:34:00.001+10:30

As far as I know, It's still only me wandering around in the territory that I call "Negmandel". I'd love to hear from anyone else who's been exploring there, and what they may have called it. It is a very strange and beautiful place.

The way that I am rendering it, is probably relatively expensive, which is both a good and bad thing depending how you look at it.

There is doubtless lots of potential for speeding things up: for one thing, most of UltraFractal's optimization is geared towards early bailout of the orbit iteration, which negmandel doesn't do at all, since all the orbits are convergent and the Mandelbrot formula that I'm using (the standard generic one) only has an upper bailout.

On the plus side, I get this feeling that I'm unearthing something rare and inherently valuable here, and it keeps my cpu's busy working on something of interest.

On the downside, because it's slower, more patience is required for fruitful exploration. It may also be a bit environmentally wasteful, if there does turn out to be a way of getting these images rendered using a millionth of the compute resources, then I'm not making very good use of the electricity.

Without further investigation into these questions, for now I feel that it is worth exploring this odd mathematical landscape and it gives me great pleasure to share these recent negMandel discoveries with you.

This first one rounded out an earlier thread of investigation by filling in some finer details through increased iteration:

I cracked open an old ("wicker") negmandel setup that produces some lovely textures like some kind of woven crystal light-fibers:

Which led to this lovely series with a sense of glowy blue light landing on yellow substrate:

Some shifts in coloring:

And some random bits and pieces - it's hard to make sense of anything coherent here - they're both intensely chaotic and orderly at the same time:

Duck Bits

2011-08-23T12:46:00.003+09:30

I've been extremely busy at work and playing with SideFX Houdini Apprentice at home, which means I haven't set up any new fractals in quite a while. Hopefully I'll get a chance to stoke up the queue soon.

Here's a wrap up of recent ducks fractals, beginning with this series of filamentous roadworks:

Here some shots of this Sierpinski-Triangle-esque shape that shows up quite frequently in Ducks fractal:

Now some broader views with a more cellular feeling about them:

Wrapping up with a couple of portrait-style views of ducks near the origin:

Ducky Times

2011-06-02T22:56:00.000+09:30

It has taken me a little while to get into the swing of Sam's Ducky fractal formula, but in a minute I'll show you some of the spots that I've been quite happy with.

This super-detailed area of fractal exploration is getting lots of attention recently, which I am very happy about, being a total space-filling fetishist!

Kali on fractalforums (Google: 'kaliset') has been doing some great work extending and modifying a ducks-esque formula, including 3d versions.

The ducks formulae generate shapes/structures that are not too far from what we see with kaleidoscopic IFS fractals (see for example see subblue's brilliant work).

On that note, check out this totally wicked in-browser webGL 3d fractal app by subblue called fractal.io. You will need a newish browser like firefox4 or current Chrome. It's well worth updating your browser just to play with this and see the awesome potential of webGL.

Kali, Sam and Softology have all been working on Ducks recently, and it has also got the attention of the fragmentarium project. It's really cool to see investigation into this new area from multiple sources.

So, here's what I've got to show, this is my first semi-reasonable looking Ducky (Julia) :

Now a couple of fairly basic duckies:

Edging up the complexity a little:

This one looks like the result of a highpass image filter, but it's not. It's the frequency-imbalanced result of iteration skipping:

In the start of this spiky series I used 'statistics' coloring (by Kerry Mitchell) which picked out some nice sharp filaments from the ducky structure:

I'm rather fond of these high-contrast spikes:

I took the spikes with me on this foray into the Koch Snowflake shapes that you see sometimes in ducky fractals, here in a palette of sandy, dark and neon:

Here the Koch Curve shape is picked out in somewhat of a woven fabric style, perhaps with South-American inspiration:

Iteration-skipping setups can really give a nice bridge between the graphic arms of the low-iteration angular spirals and the cloudiness of the high-iteration layers:

I also found some oddities:

So there we have a first taste of exploring the ducky, I'm looking forward to having a look around some of the other variants.

Iteration Skipping

2011-05-02T21:44:00.001+09:30

Fellow fractal explorer Sam Monnier has recently done great work with some interesting new space-filling fractal formulae, including a new (to me) method for coloring densely detailed fractals. The idea is to skip iterations in an otherwise normal coloring formula, which can really help to introduce variations in what details of the fractal shape are resolved. Skipping (or weighting) makes it possible to build a much more interesting structure to a composite, with isolated detail ranges contributing different aspects of the fractal shape to the final result.

In order to play with this I made modified versions of two of the coloring methods that I use a lot: Exponential Smoothing and Triangle Inequality Average. I added controls for both modulo-based iteration skipping and weighting of iterations using a cosine function. Together the two have been extremely useful and they make it possible to really change the way the color gradient is looked up by the form of the fractal.

The following is one of the most interesting things I've found using iteration skipping, it's a phoenixDoubleNova with 6 layers:

Its neighborhood, with wiggly brainy shapes:

Iteration skipping helped in these Nova fractals both to increase the chaos and make it look like something specific is happening:

These phoenixDoubleNova got some of their shape and dynamic range from skipping layers:

Pseudo-basin boundaries are sculpted by the skipping in interesting ways. The next few are from a particular Julia-lake (shown first) that overlaps the edge of a mandelfield. When these plateaux straddle the area between open lakes and closed, they apply pressure to the dynamics of the foam, preventing the pseudo-lakes from closing as fast (near the edge it takes more iterations for them to close):

Here iteration skipping gave rise to an altogether different look to the typical phoenixDoubleNova spiral network - isolating the julia foam atoms in a way that for some reason reminded me of teeth:

Nova point basins get the skipping treatment:

Some more classic phoenixDoubleNova spiral foams using skipping layers to accent the structure:

These two triangular nova-grids got some more macro-structure from the skipping:

Negmandels of Early 2011

2011-03-29T21:00:00.003+10:30

I am starting to wonder if anyone else in the world has explored this view of the generalized mandelbrot formula much. A while back I did try to add an example image to wikipedia but unfortunately it did not stick. As anyone who's tried to contribute to Wikipedia will know, it can be incredibly hard to convince the deletionists that things are notable and worth keeping.

I can understand though why negmandel is not readily accepted as notable by pure-math oriented people because the main generator for detail is not really there in the mathematics. It is rather born from the limitations of the common digital implementation of complex power (and it's reliance upon complex logarithm). Indeed, these 'branch cuts' that negmandel is so intensely covered with, can be viewed as just an artifact of the implementation -a very low level artifact- but thus of little theoretical interest.

I still think that there is something to learn from negmandel, quite apart from the gorgeous images that it is capable of producing. The adaptation of complex log into a number system that does not naturally support the representation of multivalues (nor any kind of infinity, particularly) is the folding of an infinite number of values into a fixed range. This is quite reminiscent of what a modulo function does.

It can be thought of similarly to a modulo on the phase component of a complex number. It has the effect of converting an infinite number of input values into a single finite value. Computers necessarily do this kind of range-optimization a lot, and I think there are aspects of mind that use this same type of reduction in order to make concepts more tractable. Clearly it makes quite a mess of structures that may have existed in the full 'multivalued' result of the formula. I am very interested to explore exactly what kind of mess it makes, and what traces remain of the original structures.

There are truly endless amounts of detail to explore in the negative fractional exponent mandelbrot fractal, the following are some of the shots I've taken on recent trips.

Polarized Light Fractal Microscopy

2011-02-23T15:38:00.002+10:30

More explorations of tweaking negmandel to look like colorful stained glass or polarized light microscopy.

Unfortunately even at 2048x2048 there's not enough detail for my taste, so I may return to these to crank it up a bit.

This is what the ore looks like for this type of fractal:

Dark Vegetable Negmandel

2011-02-11T14:45:00.004+10:30

Setting off again into the fragmented world of negmandel, I followed this path into the dark and collected some unique and beautiful specimens along the way.

Starting Point:

First Selections:

Tunnels:

Misc:

Branchy:

Stained-Glass Microscopy:

Bright Stringy Novas

2010-12-26T02:50:00.004+10:30

These are a series of glowing electric blue webs of spiral filaments in a red foam or froth.

The filament-style is still in development here but there were still plenty of choice nova spiral accentuations, mmm, delicious:

Skipping Forward to Stringy Curves

2010-12-26T02:20:00.003+10:30

There are other things I probably should have posted before this but I found the threads of these lovely Novas to be just so intricate and curvy, so I bring them forward thusly:

Organic Texture Nova

2010-12-01T12:54:00.003+10:30

These swatches are from an unusually textured area of the doubleHalleyNova fractal:

Thread of Foams

2010-11-22T15:04:00.003+10:30

This thread of development using a formula called "Egg" started off looking quite unassuming:

Then I found some more interestingly structured areas:

Then things started to get quite nice and intricate and unusual:

Eventually I hit this wicked vein of gorgeousness:

A couple of alternative colorings that got away from the goodness somewhat:

Found some other nice stellar spirally things on the way too:

Fertile Spiral Fields

2010-10-09T23:26:00.003+10:30

It seems that there is always something new to discover in the phoenixDoubleNova fractal, and this starting point lead to quite a lot of nice loot:

An alternate coloring:

Shallow Water Novas

2010-10-09T23:12:00.003+10:30

Not a lot of time for fractal fishing at the end of a project at Rising Sun Pictures, but our work on Harry Potter and the Deathly Hallows (part one) is now finished, hoo-ray! I was using SideFX Houdini and it was utterly fantastic to flex it in so many different ways. Houdini is truly the most powerful piece of creative software I have ever used, if you're into 3d it's well worth learning (even if the initial learning curve is close to vertical!).

Despite less time for fractals, I still got a few nibbles from phoenixDoubleNova:

Distilled AntiqueOil

2010-08-29T01:20:00.006+09:30

Here's a preview from the main queOil vein I recovered on this brief foray:

Returning to the spot, near where I have previously harvested antiqueOil and it's relatives, I have extracted some further amount of it, and came across a unique spiral queoil, as if from an ancient reptilian hide.

After restarting exploration and some relatively poor steering, these few drops of queoil were recovered:

Some nice queoily dots were uncovered:

Hints of Reptile Hide appeared:

And yielded a good quantity of delightful antiQueoil:

Lambda Mandelbrot Circles

2010-08-20T22:14:00.003+09:30

Lambda fractal has some interesting behavior for negative exponents, here we see an exponent of (-2.0, 0) at locations near (-25.225820278925, -17.834638267085) develop circular julia-foams with a highly detailed fractal dimension to them:

Construction Stripes:

TorusNova Oddity

2010-08-02T11:59:00.002+09:30

I tried a new type of nova here - the TorusNova.

It seems fairly brutal to the overall shape of the fractal - creating basins that modulate the openness of the sets in a perfectly straight wood-grain kind of texture.

Perhaps a tad geometrical but interesting I think:

These ones are halleyDoubleNova, so thet're not really related to the above, but the color pallete is nearby, and I think they're suitably strange:

Two WickerMandels

2010-08-02T11:51:00.001+09:30

A brief revisitation of my Wickermandel setup.

Negmandel Roundup

2010-08-02T11:37:00.004+09:30

I've entered a quiet period lately in terms of new fractal work, but I have quite a backlog that I haven't posted. Here's the other half of a recent negmandel spree, with some basic grouping by color theme:

Bright, greenish:

Green and Brown translucent:

Yellow Blue Fossils:

Party Time

Blue / Stone:

Texture Study:

Green and Orange:

Negmandel Revisited

2010-06-21T14:33:00.005+09:30

I've recently headed back in to the world of the extremely fragmented negmandel fractal, and some of the results are looking very interesting.

Here's something in the same vein as my last bit of fractal geology.

But I was interested to try some alternative color compositions, so I quickly veered away from this:

Here I found some very nice purple/yellow areas:

I investigated some silver/gold threads:

Green hotspots betwen the fragments:

This strangely textured yellow/green thing:

And some nice organic random formations:

Some texture studies:

Other bits and pieces:

Dendrite Julia Clouds

2010-06-17T14:34:00.003+09:30

Some older stuff that I forgot to post:

More Gems

2010-06-17T14:33:00.002+09:30

Some novaJulia gems that missed out on getting posted back in May:

Oddly Curled

2010-06-17T12:26:00.004+09:30

We're in the Nova-Julia fractal again here, finding some interesting double-bounded cloudy julia gems. They resist flooding with detail up to a certain number of iterations but then they give in, which makes it possible to do some interesting things with coloring whilst keeping the detail everywhere.

Here is the runup:

What is that spiral thing doing? Going in for a closer look:

Tailing out I began to bring in some blue to the outer parts:

Mandelfields and Surrounds

2010-06-17T11:50:00.004+09:30

Like some kind of sponge that soaks up detail, mandelfields force open the foam into little lakes, stopping detail from filling them:

This is clearly on the inside:

Whereas this is nearby on the outside:

Phoenix Foam

2010-06-17T11:36:00.001+09:30

Most of the foams I've found have been julia/mandel-esque but these two have a much more phoenix feeling to them:

NovaJulia Gems

2010-05-24T14:44:00.004+09:30

On a recent expedition into the caves of the novaJulia fractal lake, I recovered these gorgeous fractal gems:

This gem was found deep in a mandelfield crevice:

A hot sausage-gem:

A gem paired with a mandelfield:

For completeness I'll repost the gems from the first leg here:

Nova Julia Expedition Second Leg

2010-05-24T12:24:00.003+09:30

I ended up finding a great number of Julia gems which I will reserve for a separate post.

Here are some of the finest views I encountered on my return:

And some of the strangest artifacts:

Oddly encrusted puddles:

And a heap of hot translucent sections:

I jotted down these maps of the landscape too:

Nova Julia Expedition Leg One

2010-05-19T08:58:00.006+09:30

The trail along the edge of this mandelfield is scattered with these closed composite Julias that I found quite irresistible, more on them in the second leg:

In places it became too hot for the plant life to survive:

I passed formations that were translucent like some kind of soft and detailed organic crystal:

The variety of forms was compelling:

Leadup to NovaJulia Expedition

2010-05-18T15:13:00.003+09:30

This post documents the start of a recent thread of work with the Julia variant of the Nova fractal. I usually explore the Mandelbrot variants so I was hoping to find something a little different here.

To begin with I put out some maps - just to see the lay of the land:

Just above and to the left of those blue things I noticed some interesting squareish bits, so I went after those briefly:

Taking a step back I went past this interesting mandelbubble - with the main cardioid outlined. This was something I haven't seen before, so I took a look around:

A hint of things to come, I hadn't realized at this stage that each of those little embedded julias were closed and built from other tiny julias - in outer-mandelfield regions at least:

Looking back again I found this, the mandelfield at the very start of a long and fruitful trail:

What was happening on the edge? I took a closer look:

And this is where I finally clocked the first hints of something gorgeous:

Intricate Nova Web

2010-05-14T15:41:00.003+09:30

It's not everyone's taste but to me, this is one of the best bits of texture found so far in nova fractal:

Along with these came a bunch of similar but not quite as nice exploratory positions and layering setups:

Lakes Intruding:

Associated MandelFields:

Texturally similar, with color tweaks:

And a brief foray using orbit traps:

Wiggly Novas

2010-05-14T11:11:00.002+09:30

I found this area of a halleyNova that has strange wiggly features like lines with brackets at the ends:

Took it for a fair few turns around the CPU:

Nova Foams

2010-05-06T10:33:00.006+09:30

The relaxed Nova fractal MandelFields have a phenomena where the dusts of closed Julia-like shapes open up into dusts of open lakes.

Normally I avoid these areas as the flat areas are devoid of detail - what a waste of pixels! for example:

But just outside the MandelField are dusts of almost-open Julias, which I think are some of the nicest ones. This behavior will be familiar to anyone who's played with the Julia fractal, and nova illustrates it really beautifully.

I found this Julia-dust in one such area, which has a really nice compounded-complexity to it. It's not as irregular as wider areas of the nova but I like the way it is getting near to the edge of open lake territory.

Here is the path that led me to this area, I noticed a MandelField poking in at the right-hand edge of this:

So I took a portrait/mapping look at it:

Had a closer look at that main sausage,

Closer again:

A shot on one of the deltas leading into the lakes area, the glow comes from a low iteration-limit layer:

And a few more sausage-fields from an earlier experiment:

Blue Stellar Novas

2010-04-30T15:08:00.003+09:30

I found a cool brain-like pattern in a HalleyNova, (at the end of this post) but I had used imaginary power which caused some nasty seams.

So, I tried to get rid if the seams by zeroing out the imaginary part of the power. Unfortunately I didn't get the brain any more but I still found some interesting things.

These ones are kinda cloudy:

And these have chains of interestingly interwoven angular spirals:

And some more random parts of this thread:

Intricacy

2010-04-30T10:24:00.003+09:30

I took a brief excursion to another side of nova, and found these nice intricate fossils:

Nova Statistics

2010-04-29T09:29:00.003+09:30

It's nice to find another coloring method that gives a genuinely new and interesting look to the intense detail of the nova fractal. I recently discovered Kerry Mitchell's 'Statistics' coloring (in lkm.ucl) which gives some really interesting structures that blend well with Exponential Smoothing Normalized.

Here is Kerry's description from the 'Statistics' coloring source code, it says it's better suited to 'inside' coloring which is great because I spend s lot of my time in the lakes ;)

Quoted from lkm.ucl:

Statistics

This started out with an article written by Stephen Ferguson on an analysis of fractal dimension, which he based on an algorithm by Holger Jaenisch. The formulas here modify Stephen's analysis and add other standard statistical measures. Since the measures are typically used with bounded datasets, this coloring method may be more applicable as an "inside" scheme, but there's nothing stopping a user from employing it as an "outside" scheme as well.

The statistical measures implemented are: minimum, maximum, range, mean, standard deviation, coefficient of variation, and fractal dimension. All are defined only for real variables, so there are 4 choices for reducing the complex #z to a real number: real(#z), imag(#z), the magnitude of #z, and imag(#z)/real(#z). The last method is an attempt to capture the polar angle of #z, without the discontinuities involved in actually using the angle arg(#z).

Once the choice of variable has been made, the first 3 measures are simple enough to compute. Simply monitor the orbit, updating the minimum and maximum as they change. Once the iteration has ceased, the range is just (maximum - minimum). The mean is computed by keeping a running sum of the variable, then dividing it by the number of iterations.

The standard deviation is a measure of the spread of the data, and is defined in terms of the sum of the squared differences between each datum and the mean. This can also be computed by keeping a running sum of the square of the variable. This sum is used with the sum for the mean to determine the standard deviation. The coefficient of variation is a normalized standard deviation: it's the ratio of the standard deviation to the mean. Finally, the "fractal dimension" computed here is not the true fractal dimension, but an approximation to it. It's the standard deviation normalized by the range.

Aside from being texturally interesting, this setup has a gorgeous gold/blue balance to it:

Further exploration:

Blue set:

Green set:

Homegrown Organic Novas

2010-04-28T13:05:00.003+09:30

No pesticides or inorganic fertilizers were used to grow these brickus nova buds:

Getting back on the homegrown:

Black Dandylion

2010-04-20T12:20:00.005+09:30

I was poking around with other formulae trying to see if the negmandel technique might give interesting results elsewhere.

In this case I tried the 'Lambda' formula and found some awesome patterns that are reminiscent of a massive, infinite network of nodes connected to each other against a background of weak connectivity.

This reminded me of the model for the self-organization of space in an information-theoretic model of physics called Process Physics developed by Reg Cahill from Flinders University in South Australia.

The main difference of course is that in Process Physics there is no space assumed beforehand - patterns of strong connections form in a previously dimensionless matrix of connection weights. The approximate 3-dimensionality of the network has to be established later on by analysis of the connectivity.

I find PP very compelling, but the mainstream physics community seems to just completely ignore it. Possibly because it challenges some of the core beliefs that people have based their careers upon.

I can't much of the PP papers because they get very technical, but I wholeheartedly recommend giving them a try.

Also these fractals look kind of like choice black dandylion seeds:

Fragmented Domains

2010-04-20T11:13:00.003+09:30

Further abuses of the domain fragmentation potential of the common computer implementation of complex logarithm.

In English: Computers can't really cope very well with this particular bit of maths, and in their haste and confusion, masses of melted fragmented crystal chunks result:

Warm sharp spirals:

Cold, blue, subtractive areas:

Warm and intricate details:

A long study of geometric spirals and vertigo in pink:

Getting Colder:

Sharp spirals:

Grey sky and horizons:

Fractal Grab Bag

2010-04-14T14:11:00.003+09:30

A selection of some of the more oddball things I've done lately:

A closer look at the stained-glass-city-plan from a previous post.

A couple in the metallic nova vein.

Fabric-like novas:

Negmandel:

Netagive-exponent-phoenix (negphoenix), which has been properly fruitful, but these ones are just some of the more random things I found.

A map for negPhoenix exploration:

Some attempts at getting interesting things from negative exponent nova (I think I used doubleNova here).

Taking a look at negLambda - was quite pleased with the blackDandylion look of the last two:

A couple of good-old nova-iteration-ramp based setups:

An interesting brain pattern - it looks promising but unfortunately it has some seams that will need to be covered up somehow:

Fractal Geology - Serious Business

2010-04-01T11:31:00.005+10:30

Here is the map I used to find the following negmandel treasures:

The next one was an instant favorite, piles of variety and detail, in a fractured / refractive spiral. I initially had it color corrected to increase the contrast but that seemed to make it loose its appeal, so here it is in its raw an unadulterated form.

Here are some details from the above:

A messy cousin:

Some kind of lichen-covered skeletal relic:

A closeup on the lichen:

Rough triangular trees:

Another spiral:

Exploration revealed iron-ore with quartz inclusions:

And this is a detail of the above - showing an interesting arrowhead grain:

Fractal Doily

2010-04-01T11:14:00.002+10:30

Something on the floral side, I noticed some webs of spirals in this fragmented area:

So I went in for a closer look and discovered spiral doilies! :D

Illuminated Filaments

2010-04-01T10:50:00.003+10:30

Here's a series of negmandel fractals that look like light glowing through a web of filaments:

Stained Glass City Plan

2010-03-25T18:19:00.003+10:30

This took a fair while to render, but it was worth it! Like some crazy stained-glass city plan with light shining though it:

Further WickerMandelbrots

2010-03-25T18:05:00.004+10:30

Continuing some earlier investigations in a wicker-weave area of the negmandel, I've found these really delightful textures, and some interesting geometric spirals.

I'm really digging this one:

Now we start to see some hints of spirals:

And some alternative coloring methods that bring more variety:

Stony Stormy Negmandels

2010-03-25T16:54:00.005+10:30

I count this next work as a great success of organic fractalmaking - there's something very stony and cold and natural about it, I really like it:

This is from a location not too far away:

Upon seeing the following I exclaimed "this is one of my favorites of all the fractals I've ever made", it's got a little bit of everything, it's varied, subtle, organic and intricately detailed. I love it:

Here is a relative:

Some more distant relatives:

A texture study:

And here is a map of the region:

Origami Negmandels

2010-03-25T13:35:00.004+10:30

This thread of negmandel fractals started here, like some kind of fractured lightning bolt:

Further exploration revealed triangular spirals and other wire-bounded origami complexities:

I spent a fair bit of time exploring this triangular spiral, which looks like some sort of origami paper folding or something.

Negmandel Fronds

2010-03-15T13:58:00.004+10:30

Some nice threads that have branched off from recent negmandel work:

Lino Cut:

Thinker/Shards:

Sandy and Stone:

Golden Choppy Spiral:

Cyan and Translucent:

Hot Staircases:

Wicker Mandel

2010-03-12T09:31:00.003+10:30

Like some kind of infinitely detailed crystal weaving - more results from recent negmandel exploration.

Negmandel Offshoots

2010-03-08T21:01:00.002+10:30

Extensions of recent explorations in the negmandel, some gorgeous golden glows

Architectural triangular slate spirals:

And some other interesting directions:

If you would like to order a print please send me an email.

Negmandel Spree

2010-03-08T20:53:00.003+10:30

Revisiting an old favorite - the mandelbrot fractal with a non-standard exponent of -1.2. A lucky choice of coloring method has led to these incredibly intricate stained-glass like renderings.

If you would like to order a print please send me an email: gdanzoATgmail.com.

Ruby Veins

2010-02-25T12:54:00.002+10:30

Spiral veins of ruby embedded in some kind of fractal rock:

Texture Swatch

2010-02-25T12:37:00.003+10:30

So many different patterns to explore, here are some texture studies from February 2010:

String of Pearls

2010-02-25T12:19:00.002+10:30

A happy accident led to these lacey strings of glowing beads, which provide a nice contrast to the dark spirals they sit between:

Fractal Algae

2010-02-25T12:09:00.003+10:30

Algae is simplicity itself, and here is a set of straightforward novas with an algae slant to them:

Strange and Awesome

2010-02-24T15:04:00.002+10:30

Not sure why but these really hit the spot for me - so nice and odd, but somehow regular too.

Spiral Circus

2010-02-24T14:52:00.003+10:30

My lovely partner Lorikate and I have been watching Carnivale lately, which is really good if you've seen it from the first episode! There's no direct reference to it here but something of its crazily convoluted storyline, and dusty atmosphere perhaps?

Stripey Novas

2010-02-24T13:32:00.003+10:30

Intensely detailed nova fractal with stripes that accent the spirals and shape the coloring in an interesting way.

Plant Novas

2010-02-16T15:22:00.004+10:30

I got pretty hooked on this sunlight plant vibe:

Metallic Novas

2010-02-16T15:08:00.003+10:30

A series of explorations, again in the Nova Fractal, with a metallic chromatic theme.

Simple Novas

2010-02-16T14:03:00.004+10:30

Fields of spirals merging into fields of grids, with a generally blue/green kind of slant to them, and plenty of detail.

Bright, Intricate DoubleNovas

2010-02-08T15:30:00.002+10:30

Light, feathery and soft with little rainbow flares and a massive amount of detail, this series is proving to be very fruitful.

Dark, Highly Detailed Phoenixes

2010-02-08T15:14:00.003+10:30

I don't think I'll ever get tired of exploring PhoenixDoubleNova - its laces are just so gorgeous!

Sinister PhoenixDoubleNova

2010-02-04T15:47:00.003+10:30

There's something sinister about this phoenixDoubleNova:

Though it's relatives perhaps less so:

Some heading towards hippy bead-wearing territory:

Getting a day job:

And taking a turn towards a more balanced life:

DoubleNova

2010-02-04T13:34:00.003+10:30

I decided to head back into this area of DoubleNova, which has proven to be worthy of further exploration once again.

I extended those nice planty fronds to add more detail:

Detail everywhere:

Stellar:

Chromatic gravitational lensing:

Lensing Map:

Spikes and plateaus:

And some more maps:

Sandy and Oily

2010-02-04T13:27:00.003+10:30

Occasionally I like to choose random formulae from the UltraFractal database to see what I can find. I can't remember what the one I used here was called but it gave some quite nice sandy wood-grain like detailed texture:

Adding some more layers gave this nice oily looking stuff in the flatter areas that formed under a different parameter setting:

And a cantor-dust like horizon, from another randomly selected formula:

PhoenixQuintupleNova

2010-01-27T11:44:00.003+10:30

The formula is actually good old PhoenixDoubleNova, but I set the power to five - hence the quintuple. Found this nice looking flare of mandefields:

Which led to this nice looking bunch:

Some mandelfield presentations:

Dusty oddly shaped chunks:

Mostly nice results except this one which is fairly horrible in an intriguing kind of way:

Spiral Stellar Webs

2010-01-27T11:09:00.003+10:30

Continuing an earlier run of nova explorations in an area that was full of interesting things to see:

An alternative coloring for the same spot, almost looks like a different location, but it ain't:

More in the same vein:

Getting a bit more graphical:

Edging in some blues:

Getting on the green side:

Elsewhere, I found these nice spiky things:

Julia Dusts

2010-01-27T11:01:00.002+10:30

Rounding up another series of NovaMandelbrot experiments, here are two bright and detailed fields of julia-dusts:

And some nice organic triangular dusty grids:

Cloudy Archipelago

2010-01-06T09:52:00.002+10:30

I noticed something cool happening at the top of this mandelfield, like some kind of satellite photography of clouds:

So I went in for a few closer looks:

Double Nova Lucia

2010-01-05T15:50:00.005+10:30

Here's some more snapshots along paths into the nova fractal taken in UltraFractal running in Wine under Gentoo Linux.

It's mostly the doubleNova formula used here with straightforward layering setups - always at the same point and magnification. This means that what you see is a coherent composite picture of the behavior of the fractal function though different iteration limits at that location.

These spots are mostly near the edge of mandelfield lakes, that's where the transition from closed to open-set julia dusts usually happens at higher iteration limits. You can't easily distinguish from the shapes in the low iteration limit layers where the edge of the field will be, but it's there and it always seems to magically fit quite nicely within the dynamics of the preceding iterations.

Making Hay in the MandelFields

2010-01-05T15:34:00.002+10:30

While the metaSun beat down on the dry desert ion-channels in some new intel cpu hardware, some new mandelfield fruits were ripening:

First fractal rendered on Metalucia

2010-01-05T15:29:00.002+10:30

I don't actually like it that much but I thought I'd put it up just because it was the first :D

Spongy and hungry for computation

2009-12-18T16:52:00.006+10:30

I have now got a new system to install linux on and get rendering again, I will hopefully be able to post from there soon.

In the mean time I just keep staring at this one.. even though it's got detail-free areas at this number of iterations - it's just so spongy, chaotic and complex, I just dig it.

oh, and this one:

Old Negmandels

2009-12-07T15:03:00.002+10:30

My Dad has extremely generously offered to help me get a new computer so hopefully I'll be back on track rendering some fractals again soon. I think this time I won't bother with windows and will see how UF goes using Wine under Linux. UF has a 'gold' rating with Wine so it should hopefully run pretty well.

Here are some nice old negmandels (ie standard Mandelbrot formula with a negative non-integer power setting). The amount of detail due to cutting is quite extreme!

Something a bit 'shrimpy' about this one:

Some city lights:

Can't wait to render some of these really huge on a new box!

Chromatic Nova

2009-11-23T14:41:00.002+10:30

Inspired to try Mr Velocipede's chromatic rainbow technique on some detailed novas I found a few things that didn't work very well, and one spot that did seem intriguing (even if the bands are out of order - this is roughly GRB, not RGB):

The only difference between the layers (of which there are 3) is the color, which is either red, green or blue, and the iteration limit.

The Passing of Metablack

2009-11-23T14:27:00.003+10:30

My laptop has finally died, sniff... No more new fractals for a while.

Here are some of its final valiant computations:

Annotated julia froths:

Something dark I found near zero (real) somewhere:

Climbing this novaRamp again, but with popcorn this time:

Filamentous Julia froths:

Dense wooden nova transitions and superposition:

I had metablack rendering almost every minute that I had it, and it cranked out some truly fantastic images for which I am truly thankful.

Butterfly Ortn Airy Curl

2009-11-14T19:51:00.002+10:30

Ann oldie but a goodie, this spiral is intensely detailed everywhere and has a nice balance of color. This render is 8192 pixels square.

NovaRamp Zoomable

2009-11-13T23:15:00.004+10:30

Test of closer.it zoomable widget, got it the right size now I think..need to ask closr.it whether they can support square widgets! Check out the fullscreen version, it's much cooler!

Stellar Mandelfield

2009-11-11T16:11:00.001+10:30

There's something peculiarly nice about this:

Metablack in the Heat

2009-11-09T14:05:00.006+10:30

My laptop barely functions in the heat, but I still found some more sweet spots inside phoenixDoubleNova:

Some cellular structures:

In response to a post about me on the Orbit Trap Blog, I went back to one of my old setups and explored some of the area surrounding "El Dorado":

Sifting Fractal Sands

2009-11-03T11:12:00.004+10:30

A lot of visually tasteless maps (for navigation purposes) and nasty blobby things have been slowly coming off my render queue lately, but some of it has worked out okay too:

Murdered Mandelfield

2009-10-23T10:25:00.003+10:30

This cute little mandelfield has been run over by a truck:

Sunset Normalizations

2009-10-23T10:13:00.004+10:30

I've been playing with some formula tweaks - one thing I like to try is adding a blending factor that mixes between the usual iteration value and one that has been normalized (to unit length). It seems to introduce mostly anisotropic distortions which are not my favorite thing but this area did turn up some interesting landscape like spots:

Since it looked a little like some kind of planetary vista I tried to enhance the sunset feeling using direct orbit traps:

I also explored some other possibilities with these super dense filaments: