FUN WITH FRACTALS (Or: CORRECTING A RANT)

There is no easy way to segue out of my past horrible week of death and Hell  and victimization by a criminal element working from within our State government.

But being with people helps.

Bubble Lost in a

My classes.    My friends.    My grandson in that photo – in a big bubble in a pool.

 

Science helps too.   Look at the water up there in that pool.   Or:

fractal smoke

And after all my troubles  I can still smile thinking about Son and I out there in the midnight cold, doing our astronomy,   looking for the asteroid….

And then there are these things:

fractals vortex
I re-read last week’s “Saturday Rant”  about the information black-out we are generally subjected to,    and thought I should “refine”  it a little bit.   Our Rulers disagree with most of the American people, and so I wrote about how they censor information, so we think we’re alone and weak.     I had written  “…more importantly for the continued existence of our Republic which depends upon a Free Press…”  were the people in my classes who didn’t get to  see the recent March For Life demonstration.

Ha ha!!   —   Are the people in my classes so important that if THEY cannot see all of the news themselves,  our Republic might fall?   Ha Ha Ha

fractals rug

The existence of America depends upon the people I know!

fractals blue

No, really,   The people in each of my classes ARE that important.  And so are the people in any group that you know of.    The people in your family gathering.   The people in your office or shop.   A random sampling of people on the sidewalk that you are  on.    Your religious congregation.

It’s not just that ANY group of Americans are vital to the preservation of our Republic.   It’s not just that we believe that EVERY citizen is important.     Beyond that, deeper than that:

It’s the fractal dimension.
I’ve been showing you pictures of fractals.  A fractal is more than just repeating patterns.    A fractal illustrates that any one small segment or portion of something contains within it information for the whole.

That’s my non-mathematical definition.

fractal smokies

Ahhhh…the beautiful Smokies!

At the foothills of a mountain range,  pick up a tiny, tiny piece of … like, sand.     It’s a miniature rock.   And it contains within its contours and components the whole mountain range.

fractal mountains

The edges of a wave in the ocean exemplifies wave action of all waves in their totality.

fractals spiral waves

Smear some oil into a mud puddle.  (That’s the kind of science I like to do!)     Then a small penny-size portion looks just like the entire pattern of the colorful oil film.
Too many photos?

Want some math?     (This fractal thing is real.)

The math involves Julia Sets:      The function for certain Julia sets is: f(z)=z^2+c.   That’s it.   The new complex coordinate is set to the old one squared plus “c”. What is c? It is simply a complex number, and it can have any value you like. Different c values produce different Julia sets. Let’s use (1 + 1i) as c. So, if we were to start with the point (2 + 1i), the first iteration would be:

f(z)=f(2+1i)=

(2 + 1i)^2 + (1 + 1i)=

2*2 + 2*1i + 2*1i + 1i*1i + 1 + 1i=

4 + 2i + 2i + 1(-1) + 1 + 1i=

5 + 5i -1=

4 + 5i

So the first iteration brings us to (4 + 5i). We can do it again now.

f(z)=f(4 + 5i)=

(4 + 5i)^2 + (1 + 1i)=

4*4 + 4*5i + 4*5i + 5i*5i + 1 + 1i=

16 + 20i + 20i + 25(-1) + 1 + 1i=

17 + 41i – 25=

-8 + 41i

So our second iteration gives us (-8 + 41i). We continue to do this . . . .
xxx

Thanks to  this Website …

http://www.angelfire.com/art2/fractals/lesson2.htm

 

Don’t forget the point I was making.   (I almost did!)    Enjoy the pretty pictures.  Look up some more fractals on the Web.   But remember,  my classes,  or any group of people:    each person in your life,  is   “like”  a fractal.    They are representative of the whole.   Thus:

You cannot “love the world.”   Love the person next to you.

You cannot “feed the hungry”  Feed the hungry one next to you.

You cannot rail against censorship and ignorance.   Inform the friend who you are talking with.   Spread the word.  Spread the truth about your Creator, without fear.   Spread the truth about our wonderful country (or your wonderful nation).   Spread the truth about morality and virtue and good citizenship.   Spread the word that Life is to be cherished and protected and celebrated.

Our Rulers do not.

It’s up to us to stop censorship and political correctness.

Each of us is important.   Each of us is representative of the whole.

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Explore posts in the same categories: 2015 Issues, Astronomy, Christian Analysis, Citizen of this world, Cooper, Current Events, Science Fun, The necessity of Virtue

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