Fractals are the Mogao Caves of our times

One of the many illustrated caves

One of the many illustrated Mogao Caves in northwestern China

Alright, maybe it’s just me but the image above and just about everything else in the Mogao Caves bears a strong visual resemblance to what I see in fractal programs.

What I see in fractal programs:  That might be a new way of defining the term but I believe it’s the most relevant in the context of visual art. This is because fractal formulas when rendered exhibit a discernible style to them just like the work of a painter like Van Gogh or Gustav Klimt or an architect like Frank Lloyd Wright does.  Think of all fractal images as the work of just one artist: would you not suspect he was possibly inspired by the type of artworks we see in the Mogao Caves?

Fractal made in Sterlingware 1.7

So, what are the visual similarities?  What’s the family resemblance between the Buddhist cave and the fractal image?

Visual similarities

  • Symmetry (left/right mirror image)
  • Hierarchical structure (the details support the “macro-tails”)
  • Geometric (circles, squares, parabolas, shapes that are formulaic)
  • Abstracted/Symbolic (simplified and stylized but retaining a resemblance to real things, mainly natural: hills, sky, clouds, flowers,)

It’s not just the visual style resemblance; illustrated caves seems to work like fractal programs too.

Viewing environment similarities (caves and fractal programs, in general)

  • Immersive (walk into a cave; zoom into a fractal)
  • No frame (the whole image is uncontained and unconfined)
  • Interactive (your head’s the frame; turn the head, change the composition; focus on a detail in a corner or the main structure in the center, or something you never noticed before)
  • Variations on a theme (we see repeating shapes and structures; visual deja vu)
  • No distractions (related to immersive; one can easily lose track of time, and space, in fractals because there is no real beginning or end; same for an illustrated cave)

Notice the little, tiny buddha-circles on the side walls in the photo and the little red, dot-balls in the central area of the fractal, one the “walls” of the fractal?  Obviously there’s no close fractal equivalent to the human form so all we can compare the statue of the Buddha in the center of the cave with is the prominent central shape that occurs very often in fractal images (especially in Sterling).  In this fractal it appears to be breaking out of a clearing in the clouds which frame it’s “head” like a garland of flowers or crown of brilliant clouds.

Another of the Mogao Caves

Another of the Mogao Caves


Another of the Sterlingware Caves

Another of the Sterling Caves

The similarity comes from more than just the three niche elements; although you will notice that the fractal niches are all proportional and complimentary to each other like they are in the cave example.  This is what I mean when I’ve said in previous postings that certain kinds of imagery are natural for fractal formulas to make.  Symmetry, hierarchical order, and profuse detail and ornamentation come naturally to fractal images.  The Buddhist art in the Mogao Caves (and elsewhere) exemplifies these same visual aspects for religious reasons to convey and express religious ideology.  The are, in a sense, what I would call “Divine Diagrams” and it should come as no surprise to anyone familiar with fractals that fractal images often bear the same elements but, naturally, in a generic way.  Fractal images could easily be used for symbolic purposes in a number of religious contexts.

One interesting bit: notice in the fractal, below each of the niches, there are similar “stains” just as one sees below the niches in the cave photo.  Perhaps it’s from burning candles or food offerings or some sort of weathering?  In the fractal, of course, it’s just part of the formula rendering.

A couple other similarities to point out:

  • there is a vertical line structure/feature extending up above the central niche in both the photo and the fractal
  • all three niches have a framing element to them including a large, expanded framing element overtop of them in both images
  • extending up from the two minor niches in the fractal are two obvious lines which meet a horizontal line just above them.  This corresponds, to some extent, to the wall corners and the border of the edge of the ceiling in the cave image.  It’s just a fluke that the fractal should look like it’s got walls and a ceiling but it’s expected that one should find such geometric elements in a fractal; in the cave they’re just ornamentation of the room’s structure which in this cave is square, rather than round.
  • Notice what could pass as doorways on either side of the fractal on the edge of the image in line with the niches and real doorways in the photo.
  • The geometrical, architectural element of the ledge in front of the cave’s niches is also found below the fractal’s niches.  Again, geometric shapes occur naturally and frequently in fractals which cause them to easily support an architectural analogy because architecture is almost always geometrical.


Mogao Cave painting

Mogao Cave painting


Fractal Cave painting

Fractal Cave painting


Visvarupa Lokeshvara; not from the Mogao Caves but still Buddhist (or Hindu?)

Visvarupa Lokeshvara; not from the Mogao Caves but still Buddhist or Hindu or both.

Some of the same similarities occur here with respect to shapes, frames, borders, hierarchy; I think you get the idea now.  I added the last one, a statue from somewhere, because it really emphasizes the design similarities between fractal imagery and these Buddhist paintings and statues.  The last one looks so much like the fractal image that it’s hard to believe it came first.  But this is my big point: the type of imagery that fractal programs produce has existed for centuries in the form of Buddhist religious imagery.  And, if you’re familiar with religious art in general, many forms of religious art and symbolism have this fractal program resemblance .  In fact, it has no particular correlation with any one religion, I just happened to notice it for the first time while browsing the Mogao Caves on the Wikipedia.

I’m sure I’m not the first person to notice this fractal art / religious art connection.  In my next post I expand the comparison of fractal imagery with the whole spectrum of religious art showing that the elements and style of religious art are in fact inherently fractal and therefore the sort of visual art that fractals produce easily, prolifically and to perfection.