Deepest Desire...

Opening our Heart wide, we turn to the perfect highest awakening.
We are resolved to attain understanding,
to realize deep love & compassion,
to practice diligently,
transforming our own suffering &
that of all species.

All the merits of body, speech & mind I want to direct
to be part of the happiness of all people &
all species.

This is my deepest desire.

Apart from the Bodhicitta ( highest awakening ),
Apart from the thirst for Great Understanding,
Apart from the vow to Love Deeply,
I have no more desires.

~ Buddhist Chant ( rendered by Thich Nhat Hanh )

Fractals in Nature

A fractal is generally "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole," a property called self-similarity. A mathematical fractal is based on an equation that undergoes iteration, a form of feedback based on recursion.Because they appear similar at all levels of magnification, fractals are often considered to be infinitely complex. Natural objects that approximate fractals to a degree include clouds, mountain ranges, lightning bolts, coastlines, snow flakes, even various vegetables (cauliflower and broccoli).

One of the most famous deterministic fractals was described by Von Koch and is called the Koch Curve. Consider starting with a single straight line that we will call the initiator.

The initiator

_______________

Next is to define a generator, or production rule, that states "Take the initiator, scale it down by a factor r=1/3, make N=4 copies and replace the initiator by these scaled down copies, oriented as shown".

The Generator

The generator is repeated...

and repeated...

and repeated.....

etc.....

After an infinite number of repetitions this curve will be everywhere non-differentiable and will also have infinite length.

Meet some of the most beautiful fractals found in nature.

Cauliflower

This is "Chou Romanesco" cauliflower.A special type of broccoli, this cruciferous and tasty cousin of the cabbage is a particularly symmetrical fractal.

Broccoli

Though not as famously geometric as its relative the Romanescu, broccoli is also a fractal.

Fern

The fern is one of many flora that are fractal; it’s an especially good example.

Fractal Tree

Pair of trees, grown from fractals.

Human Lung

Human lung, composed entirely of fractal algorithms.

Lightning

Lightning’s terrifying power is both awesome and beautiful. The fractals created by lightning are fascinatingly arbitrary and irregular.

Mountain Ranges

Both shorelines and mountain ranges are considered loosely fractal.

Peacock

Males of both the white peacock and standard peacock variety are resplendent examples of fractals in the animal kingdom.

Sea urchins and sea stars

Sea urchins are compact, almost artistic little creatures; sea stars are more commonly referred to as starfish.

Sea Shells

The nautilus is one of the most famous examples of a fractal in nature. The perfect pattern is called a Fibonacci spiral.

Shorelines

This stunningly complex fractal shoreline is none other than the pan handle of Florida.

Darkness...

Quiet friend who has come so far,
feel how your breathing makes more space around you.
Let this darkness be a bell tower
and you the bell. As you ring,

what batters you becomes your strength.
Move back and forth into the change.
What is it like, such intensity of pain?
If the drink is bitter, turn yourself to wine.

In this uncontainable night,
be the mystery at the crossroads of your senses,
the meaning discovered there.

And if the world has ceased to hear you,
say to the silent Earth: I flow.
To the rushing water, speak: I am.

~ Rainer Maria Rilke ( Sonnet XX1X )

Seasons...

In the chequered area of human experience, the seasons are all mingled as in the golden age: fruit and blossom hang together; in the same moment the sickle is reaping and the seed is sprinkled; one tends the green cluster and another treads the wine-press. Nay, in each of our lives harvest and spring-time are continually one, until Death gathers us and sows us anew in his invisible fields.

~ George Eliot ( Daniel Deronda, Chapter LXX )

Bare Earth...

Does anyone write something on a place
that has already been written over?
Or plant a sapling where one already grows?

No, he seeks a blank piece of paper
and sows the seed where none has yet been sown.

Sister, be bare earth;
be a clean piece of paper untouched by writing,
that you may be ennobled by the pen of revelation,
so that the Gracious One may sow seed within you.

~ Rumi

Majestic Peace...

In the heart of thunder plays the melody --
To its rhythm I awake!
I get drunk with that life
Hidden in the core of death,
To the sound of the tempest's roar
My heart dances in joy.
Tear me away from the lap of ease,
Plunge me into the depths
Where majestic Peace reigns,
In the midst of restlessness.

~ Tagore

Offering of Love...

Follow the only truth --
the offering of Love.
You will then see a helpful, loving
society reveal itself.
A beautiful world will emerge before
your eyes.
One no longer strives to take but simply
opens up.
Accepting all that Love gives --
unconditionally.
In the Love is the victory.

~ Master Li Jun Feng (from the book "Sheng Zhen Wuji Yuan Gong -- A Return to Oneness")