NEW DEVELOPMENTS INVOLVING
THIS WATER LINE BREAK NEAR YALE
AND APACHE.
CREWS ARE WORKING ON ONE AND
THEN THERE WAS ANOTHER BREAK
NEAR 4th AND BOULDER.
Reporter: LOOK AT THAT WATER
SHOOTING INTO THE SKY.
THE CONTRACTOR HAD TO STOP FOR
SEVERAL HOURS WHILE THESE GUYS
WORKED TO FIX THE BREAK.
THE CITY SAYS ABOUT A HANDFUL
OF CUSTOMERS WERE IMPACTED BY
THIS BUT TRAFFIC WAS NOT
BECAUSE WHERE THE LINE BROKE,
THAT SIDE OF THE ROAD WAS
ALREADY CLOSE.
BUT DOWNTOWN AT BOULDER AND 4th
STREET, IT IS A DIFFERENT
STORY. I CAME THROUGH AND THAT
STREET WAS BLOCKED OFF BY THE
TRUCKS.
Reporter: THE ROAD WAS
CLOSED MONDAY NIGHT AND IT IS
STILL CLOSED THIS EVENING
BECAUSE OF A FOUR INCH
WATERLINE LEAK.
KAREN ALWAYS STATE FINGER HOUSE
AND SHE SAYS THE BUSINESS HAS
BEEN HERE FOR SIX YEARS AND SHE
HAS SEEN DOZENS OF WATER LINE
BREAKS. BUT SHE SAYS THE ROAD
USUALLY REOPENS WHEN THE LINE
IS FIXED AND THAT IS NOT THE
CASE THIS TIME. THE PAVEMENT
HAS TO BE REPAIRED THIS TIME.
THE CONTRACTOR DIDN'T COME OUT
TO PUT DOWN NEW CONCRETE AND
NOW THEY HAVE TO OVERLAY THE
ROAD WITH ASPHALT AND THAT
CANNOT BE DONE UNTIL WEDNESDAY.
THE ROAD WILL NOT BE OPEN UNTIL
WEDNESDAY AFTERNOON, AT THE
EARLIEST.
AND SAYS THIS IS NOT GOOD FOR
HER BUSINESS.
I HAVE TUESDAY CUSTOMERS AND
I HATE TO SEE THEM MISSING
THEIR BACON CHEESEBURGERS.
Reporter: THE WATER IS BACK ON
WERE BOTH WATER LINE BREAKS
For more infomation >> VIDEO: Water spews after north Tulsa break - Duration: 2:02.-------------------------------------------
My First Video!!! - Duration: 1:20.
9 of Hearts
Thx for watching!!
-------------------------------------------
Video: Tom Messner is looking for snow for the Wednesday AM commute. 1.31.17 - Duration: 4:33.
AND RESTORE THE
ORIGINAL GONDOLA.
ORIGINAL GONDOLA. TOM: THAT WOULD BE FANTASTIC IN
TOM: THAT WOULD BE FANTASTIC IN NEW YORK.
NEW YORK. I HEARD THE SKATING WAS GOOD,
I HEARD THE SKATING WAS GOOD, BUT IT WAS COLD, BUT THEY HAVE
BUT IT WAS COLD, BUT THEY HAVE BEEN MAKING SNOW.
BEEN MAKING SNOW. WE HAVE NATURAL SNOW AND WE WILL
WE HAVE NATURAL SNOW AND WE WILL GET MORE.
GET MORE. DO YOU KNOW HOW COLD IT WAS?
DO YOU KNOW HOW COLD IT WAS? BRIAN: COLD.
BRIAN: COLD. 13?
13? STEPHANIE: FOUR.
STEPHANIE: FOUR. TOM: IT WAS NINE!
TOM: IT WAS NINE! WE HAVE YOU COVERED.
WE HAVE YOU COVERED. EVER SEE "QUIZ SHOW," THAT WAS
EVER SEE "QUIZ SHOW," THAT WAS COOL.
COOL. BIG CHEATERS.
BIG CHEATERS. NORTHERN NEW YORK IS WHERE IT
NORTHERN NEW YORK IS WHERE IT WAS THE COLDEST AT 19 BELOW IN
WAS THE COLDEST AT 19 BELOW IN SARANAC, AND YOU GET INTO THE
SARANAC, AND YOU GET INTO THE POSITIVE TERRITORY.
POSITIVE TERRITORY. CERTAINLY NOT FOR EVERYONE.
CERTAINLY NOT FOR EVERYONE. WE HAD NEGATIVE NUMBERS IN
WE HAD NEGATIVE NUMBERS IN NORTHEAST KINGDOM AND THE
NORTHEAST KINGDOM AND THE TEMPERATURES ARE EASY TO TAKE,
TEMPERATURES ARE EASY TO TAKE, 26 IN BURLINGTON AND 24 IN
26 IN BURLINGTON AND 24 IN PLATTSBURGH AND 20'S IN MUST
PLATTSBURGH AND 20'S IN MUST PLACES, WITH SOME EXCEPTIONS
PLACES, WITH SOME EXCEPTIONS ALONG THE NORTHERN TIER IN
ALONG THE NORTHERN TIER IN NEWPORT AND MONTREAL.
NEWPORT AND MONTREAL. IF YOU ARE STEPPING OUT IN THE
IF YOU ARE STEPPING OUT IN THE CHAMPLAIN VALLEY, YOU WILL BE IN
CHAMPLAIN VALLEY, YOU WILL BE IN GOOD SHAPE.
GOOD SHAPE. PARTLY CLOUDY AND LESS THEN AN
PARTLY CLOUDY AND LESS THEN AN HOUR, AT MID-50'S BUT A LOT OF
HOUR, AT MID-50'S BUT A LOT OF CLOUDS BY A COUPLE OF HORSES
CLOUDS BY A COUPLE OF HORSES FROM THEN SO FIGURE 9:00 AND
FROM THEN SO FIGURE 9:00 AND 11:00 AND THICKENING UP BECAUSE
11:00 AND THICKENING UP BECAUSE THE SYSTEM TO THE WEST WILL
THE SYSTEM TO THE WEST WILL CONTINUE TO AFFECT US AND
CONTINUE TO AFFECT US AND RESEARCH UP IF YOU WANT TO CULL
RESEARCH UP IF YOU WANT TO CULL IT THAT BECAUSE IT WILL GO SOUTH
IT THAT BECAUSE IT WILL GO SOUTH OF US AND KICK THE HIGH PRESSURE
OF US AND KICK THE HIGH PRESSURE OUT OF HERE AND THAT HELPED WITH
OUT OF HERE AND THAT HELPED WITH THE SUNSHINE TODAY AND THIS TAKE
THE SUNSHINE TODAY AND THIS TAKE OVER.
OVER. THIS COMES ON THROUGH, WE HAVE
THIS COMES ON THROUGH, WE HAVE SNOW AROUND HERE LATE TONIGHT
SNOW AROUND HERE LATE TONIGHT INTO TOMORROW
INTO TOMORROW IT IS LIGHT SNOW.
IT IS LIGHT SNOW. NOT A MAJOR STORM.
NOT A MAJOR STORM. BUT THE TIMING IS STINKS.
BUT THE TIMING IS STINKS. THE COMMUTE WILL HAVE SNOW
THE COMMUTE WILL HAVE SNOW COMING DOWN SO BE AWARE OF SLICK
COMING DOWN SO BE AWARE OF SLICK ROADS.
ROADS. WE HAVE A COLD FRONT MOVING
WE HAVE A COLD FRONT MOVING THROUGH BEHIND THIS.
THROUGH BEHIND THIS. IT WILL THEN BE COLD AROUND HERE
IT WILL THEN BE COLD AROUND HERE AGAIN.
AGAIN. IT IS ALL RELATIVE.
IT IS ALL RELATIVE. IT HAS BEEN VERY, VERY WARM IN
IT HAS BEEN VERY, VERY WARM IN JANUARY.
JANUARY. >> STORM TRACKER, THE MAIN EVENT
>> STORM TRACKER, THE MAIN EVENT TO THE SOUTH IN SOUTHERN NEW
TO THE SOUTH IN SOUTHERN NEW ENGLAND WITH AN ADVISORY IN
ENGLAND WITH AN ADVISORY IN AFFECT AND PLACES LIKE BEST AND
AFFECT AND PLACES LIKE BEST AND TOWARD PROVIDENCE AND HARTFORD
TOWARD PROVIDENCE AND HARTFORD LOOKING FOR 1 TO 3 INCH AND THE
LOOKING FOR 1 TO 3 INCH AND THE TEAMING IS BAD BECAUSE IT IS THE
TEAMING IS BAD BECAUSE IT IS THE AFTERNOON AND EVENING COMMUTE
AFTERNOON AND EVENING COMMUTE HAPPENING NOW.
HAPPENING NOW. TO THE WEST, YOU CAN SEE THE
TO THE WEST, YOU CAN SEE THE REMNANTS OF THE SYSTEM SO A LAST
REMNANTS OF THE SYSTEM SO A LAST SNOW AROUND THE GREAT LAKES.
SNOW AROUND THE GREAT LAKES. NOT GREAT DEPTHS BUT A LOT OF
NOT GREAT DEPTHS BUT A LOT OF AREAS WITH SNOW.
AREAS WITH SNOW. TOM MORNING, WE COULD HAVE LIGHT
TOM MORNING, WE COULD HAVE LIGHT SUNNY.
SUNNY. IT IS.
IT IS. CAN DOWN.
CAN DOWN. EVEN AT 8:00 AND IT STARTS
EVEN AT 8:00 AND IT STARTS BEFORE THAT.
BEFORE THAT. A CHANCE FOR SNOW SHOWERS AT
A CHANCE FOR SNOW SHOWERS AT NOON.
NOON. THEN A LOT OF CLOUDS.
THEN A LOT OF CLOUDS. MOST OF THE SNOW IN THE FIRST
MOST OF THE SNOW IN THE FIRST HALF OF THE DAY.
HALF OF THE DAY. WE ARE LOOKING AHEAD AT 8:30 NOT
WE ARE LOOKING AHEAD AT 8:30 NOT MUCH GOING ON BUT WATCH HOW THE
MUCH GOING ON BUT WATCH HOW THE CLOUDS THICKEN UP WITH THE SUNNY
CLOUDS THICKEN UP WITH THE SUNNY FOR THE COMMUTE.
FOR THE COMMUTE. THE EVER HEAVIER STUFF OR THE
THE EVER HEAVIER STUFF OR THE MOTHER STEADY STUFF IS EAST THE
MOTHER STEADY STUFF IS EAST THE CHAMPLAIN VALLEY AT 7:00
CHAMPLAIN VALLEY AT 7:00 TOMORROW MORNING AND IT IS
TOMORROW MORNING AND IT IS LIGHTENING UP BY THE AFTERNOON
LIGHTENING UP BY THE AFTERNOON AND, STILL, SNOW TO THE WEST
AND, STILL, SNOW TO THE WEST BECAUSE OF WHAT IS HAPPENING
BECAUSE OF WHAT IS HAPPENING WITH LAKE ONTARIO WHERE WE ARE
WITH LAKE ONTARIO WHERE WE ARE EXPECTING A BUNCH OF LAKE-EFFECT
EXPECTING A BUNCH OF LAKE-EFFECT SNOW.
SNOW. THE THURSDAY GROUNDHOG DAY WE
THE THURSDAY GROUNDHOG DAY WE ARE LOOKING GOOD AND THE
ARE LOOKING GOOD AND THE LAKE-EFFECT SNOW IS RAMPING UP
LAKE-EFFECT SNOW IS RAMPING UP AS WE GET INTO FRIDAY WITH THE
AS WE GET INTO FRIDAY WITH THE LICK AFFECT SNOW COMING INTO THE
LICK AFFECT SNOW COMING INTO THE ADIRONDACKS BUT MOST OF US ON
ADIRONDACKS BUT MOST OF US ON FRIDAY, MORE CLOUDS THAN
FRIDAY, MORE CLOUDS THAN SUNSHINE BUT NOT A LAST SNOW.
SUNSHINE BUT NOT A LAST SNOW. HOW MUCH SUNNY THIS TIME?
HOW MUCH SUNNY THIS TIME? ABOUT 1 INCH IN THE CHAMPLAIN
ABOUT 1 INCH IN THE CHAMPLAIN VALLEY AND MORE HEADED TO THE
VALLEY AND MORE HEADED TO THE SOUTH.
SOUTH. IT IS ALL ABUT THE TIMING.
IT IS ALL ABUT THE TIMING. THICKENING CLOUDS, AND LIGHT
THICKENING CLOUDS, AND LIGHT SNOW AT DAWN TOMORROW MORNING,
SNOW AT DAWN TOMORROW MORNING, AND WE WILL CALL IT A SLOW OF 17
AND WE WILL CALL IT A SLOW OF 17 IN THE CHAMPLAIN VALLEY.
IN THE CHAMPLAIN VALLEY. GETTING INTO THE 30'S IN THE
GETTING INTO THE 30'S IN THE CHAMPLAIN VALLEY BUT MOVING TO
CHAMPLAIN VALLEY BUT MOVING TO THE SOUTH IT WILL BE WARMER THAN
THE SOUTH IT WILL BE WARMER THAN THAT WITH LIGHT SUNNY.
THAT WITH LIGHT SUNNY. 31 TOMORROW.
31 TOMORROW. GROUNDHOG DAY.
GROUNDHOG DAY. COMING UP ON THURSDAY.
COMING UP ON THURSDAY. PARTLY SUNNY.
PARTLY SUNNY. A HIGH OF 26 WITH MORE CLOUDS
A HIGH OF 26 WITH MORE CLOUDS THAN SUN.
THAN SUN. PARTLY SUNNY ON SATURDAY.
PARTLY SUNNY ON SATURDAY. BETTER CHANCE FOR SNOW SHOWERS
BETTER CHANCE FOR SNOW SHOWERS ON SUNDAY.
-------------------------------------------
VIDEO: County seeks input in taxpayer-funded project - Duration: 1:48.
ALL NEW TONIGHT AT 6:00
P.M., A VISION PLAN IS SET TO
GET UNDERWAY BUT YOUR INPUT IS
STILL NEEDED.
RICK MARANON IS REPORTING LIVE
ON HOW YOU CAN SHARE YOUR
THOUGHTS IN LESS THAN ONE
HOUR Reporter: VOTERS APPROVE
THE FUNDING SOURCE FOR THIS
BACK IN THE FALL. BUT THEY WANT
TO KNOW IF THIS IS SOMETHING
YOU LIKE.
WHILE MANY CITIES WORK ON THEIR
VISION TAX PLANS, TULSA COUNTY
WANTS YOUR OPINION.
WE WANT A LOT OF PUBLIC
INPUT IF WE CAN. THE PUBLIC
WILL BE THE USERS AND THEY CAN
HELP US. Reporter: THE
O'BRIEN PARK RECREATION CENTER
IS NOT SEEN ANY IMPROVEMENT
SINCE THE 1970S THAT WILL
CHANGE THIS YEAR.
THE LAST TIME THE EXTERIOR
WAS RENOVATED WAS IN THE 70s
AND THE BUILDING HAS BEEN
STANDING SINCE 1964.
Reporter: THESE ARE THE
DESIGNS FOR THE NEW RECREATION
CENTER AND THIS POOL IS
REPLACED WITH A SPLASH PAD.
TULSA COUNTY WANTS TO MAKE SURE
THAT PEOPLE WILL USE THESE
THINGS.
I AM HOPING THAT PEOPLE WILL
BE EXCITED ABOUT THIS LIKE WE
ARE . IT IS A REAL POSITIVE
MOVE FOR THE PARK AND THE
CENTER.
Reporter: BEFORE THEY TEAR
INTO THE REC CENTER, THE
MEETING TONIGHT WILL TAKE PLACE
IN THE REC CENTER AT 7:00. IF
YOU WOULD LIKE TO GIVE YOUR
-------------------------------------------
VIDEO: Grant helps Tulsa County cut down on DUI - Duration: 1:20.
THE SUSPECT OFFERED HIM $100 TO
HIDE OUT.
WE ARE PUTTING TOGETHER THAT
INTERVIEW FOR YOU FOR FOX NEWS
AT 6:00.
SHARON PHILLIPS EXPLAINS
HOW MANY PEOPLE THE POLICE HAVE
ARRESTED AFTER GETTING A
GRANT. THEY HAVE MADE 474 DUI
ARREST SINCE JULY. THE GOAL IS
TO STOP DUI INJURIES, ACCIDENTS
AND DEATHS. THE SHERIFF'S OFFICE
SAYS IT IS WORKING.
THEY HAVE CALLS FOR DOMESTICS
AND BURGLARY CALLS AS WELL THAT
THIS GRANT ALLOWS 20 OFFICERS
TO GO OUT WHO VOLUNTEER THEIR
TIME LOOKING FOR INTOXICATED
DRIVERS.
YOU CAN START AS EARLY AS
2:00 IN THE AFTERNOON AND START
PICKING UP DUIS NOW . IT IS SAD
BUT IT IS TRUE. Reporter:
THERE ARE STRICT GUIDELINES
THAT EACH AGENCY HAS TO FOLLOW.
-------------------------------------------
VIDEO: People of different faiths gather in Green Country to offer support amid immigration ban - Duration: 2:28.
WE ARE STAYING ON TOP OF A
DEVELOPING STORY.
THE EXECUTIVE ORDER ON
IMMIGRATION.
TODAY PEOPLE GATHERED IN GREEN
COUNTRY TO SHOW THEIR SUPPORT.
LET'S GO TO RICK MARANON FOR
MORE . Reporter: THERE WERE
SOME MUSLIM LEADERS THAT SAID
LOCAL CAMPUS WILL BE IMPACTED.
SOME PASTORS SAY THIS ACTION
KEPT JOSEPH AND MARY OUT OF THE
INN BEFORE THE BIRTH OF JESUS.
EMPATHY, THE DICTIONARY DEFINES
IT AS A PERSON THAT ASSOCIATES
WITH THE FEELINGS OF ANOTHER.
THIS AFTERNOON MANY PEOPLE MET
AT THE ISLAMIC SOCIETY THAT ARE
READY TO FIGHT FOR LOCAL
MUSLIMS.
ALTHOUGH THE TRUMP
ADMINISTRATION INSISTS IT'S
RECENT EXECUTIVE ORDER IS NOT A
MUSLIM MAN, THERE ARE SOME IN
TULSA THAT SAYS THIS IS NOT
JUST A PROBLEM FOR THE CITIES.
THIS TEMPORARY AND OF
MUSLIMS ALONE APPEARS TO BE A
RELIGIOUS TEST.
Reporter: NOW PLANS WITH
FAMILIES OVERSEAS ARE BEING
CANCEL.
LEADERS FROM OTHER FAITH SAY
THIS ORDER IS RUBBING THEM THE
WRONG WAY AS WELL.
MANY REFUGEES FROM TERRORISM
WENT TO EGYPT AND SOMEBODY TOOK
THEM IN.
Reporter: MANY SAY THEY FEEL
THE EMPATHY.
YOU ARE PART OF THIS
COMMUNITY.
WE CARE ABOUT YOU.
WHEN YOU HURT, WE ALL HURT.
Reporter: AN ENTIRE GROUP
SAYS PROTESTS ON THE STREET ARE
GREAT FOR RALLYING LOCAL
SUPPORT.
HOWEVER IF YOU WANT TO MAKE A
DIFFERENCE, CONTACT YOUR MEMBER
OF CONFERENCE -- CONGRESS
-------------------------------------------
Fractals Video - Duration: 18:44.
The following presentation describes what Fractals are, the history of Fractals, and
how fractals relate to global warming, medicine, nature, and art. A fractal is a curve or geometric
figure, each part of which has the same statistical character as the whole. Fractals are useful
when looking at patterns that recur in progressively smaller scales and in describing partly random
or chaotic phenomena. A simple fractal often observed when trying to understand this concept
would be the Koch snowflake. The Koch snowflake is so named for its Mathematician maker, Helge
von Koch, who was born January 25, 1870 in Stockholm Sweden. Illustrations of the iterative,
progressions of the snowflake are demonstrated here.This is a demonstration of how to create
the Koch Snowflake. This fractal starts as an equilateral/equiangular triangle. An equilateral/equiangular
triangle is a three sided figure in which all sides are of equal length and all angles
have a measure of sixty degrees. From this point the progression begins. Remove the inner
third of each side of the triangle and build another equilateral triangle where the middle
thirds were removed. This makes the second progression. The third progression continues
in a similar fashion. Replace the inner third of each side with another equilateral triangle.
This process can be repeated an infinite number of times. A key feature that applies to all
fractals, seen in the snowflake example, is self-similarity. In other words, if you zoom
in on a very small portion of the fractal, it looks very similar to every other part
of the fractal. A tree can be described in this way. When zooming into a part of a tree,
such as a branch with twigs, it would look very similar to the trunk and its branches.
The illustrations demonstrate the self-similarity a tree might have. Each progression from left
to right zooms more closely than the previous image, yet each image still looks very similar
to the last. This self-similarity can be seen in many aspects of nature from rivers, to
mountains, to seashells and to clouds. Another fractal that is well known is the Cantor Set
or Dust. The creator, Georg Cantor, was born March 3, 1845 in St. Petersburg, Russia. He
became fascinated with the fact that there are an infinite number of points on any particular
line segment. The Cantor Set attempts to demonstrate what happens when an infinite number of line
segments are removed from an initial line interval. The Cantor Set starts with the interval
[0,1], which means, the points 0 and 1 are included in the interval, as well as every
point between. Then, from this line segment, remove the middle third or the interval [1/3,
2/3]. This dust is now called a triadic set. Then, with the two new lines present, remove
the middle third from each. The Sierpinski Gasket, was created by the famous Mathematician,
Waclaw Sierpinski, who was born March 14, 1882 in Warsaw Poland. We will explore 3 ways
of creating the Sierpinski Gasket. One way to make this fractal, is by starting with
a flat plane consisting of points P1, P2, and P3. Then, pick a point anywhere on the
plane. Now randomly choose any of the original 3 points and draw an infinitely small point
in the middle of the distance between the chosen point and the original point. Continue
this process using the new infinitely small point and another randomly chosen original
point. All the points in this generation lay within
the triangular boundary that points P1, P2, and P3 make. However, the strange part is
that there are large sections within the triangle that never contain any points. The distribution
of points form a 2D Sierpinski Gasket as shown, each image from left to right containing more
and more points. Another way to generate a 2D version of the Sierpinski Gasket is by
starting with a triangle and cutting a new triangle out of the middle, resulting in the
creation of 3 solid triangles and one cut out triangle. The triangle that is cut-out
was formed by selecting the midpoints on each side of the original triangles. Then, those
midpoints were used as the vertices of the inscribed triangle. Repeat this process with
the 3 solid remaining triangles. The third method of creating the Sierpinski Gasket encompasses
the use of Pascal's triangle. To create the Sierpinski Gasket using Pascal's Triangle,
every odd number in the progression of the illustration shown, must be included in the
gasket, while every even number will not be included.
A fractal that is closely related to the Sierpinski Gasket is called the Sierpinski Carpet.
The Sierpinski Carpet is a very important fractal when dealing with antennae. This fractal
is used in technology such as cell phones, tablets, high-tech watches and computers.
It is used to organize the antennae as well as allowing for additional signals to be received.
It is important to realize that in addition to using fractals to create more efficient
antennae, fractals were being founded in other places in the 1980's. For instance, at IBM
disruptive frequencies were preventing the transmission of computer data over telephone
lines. The frequencies were simulated and mathematicians noticed that within these frequencies
there were smaller frequencies of similar form, and of course self-similarity meant
that fractals must be present. Global warming is an increase in the earth's average atmospheric
temperature that causes corresponding changes in climate, which may result from the greenhouse
effect. The greenhouse effect is an atmospheric heating phenomenon, caused by short-wave solar
radiation being readily transmitted inward through the earth's atmosphere but longer-wavelength
heat radiation less readily transmitted outward, owing to its absorption by atmospheric carbon
dioxide, water vapor, methane, and other gases. Basically, rising levels of carbon dioxide
are causing concern. This is where trees play an important role. Trees, as well as other
plants, absorb carbon dioxide for the process of photosynthesis. In other words, the more
trees there are the less carbon dioxide in the air and the less global warming will occur.
Using fractal dimensions to describe trees and further entire forest ecosystems, may
assist us in understanding the amount of carbon dioxide being absorbed throughout the world
and the number of plants that need to be grown in order to put a stop in global warming,
or at the very least, to slow down the global warming process. The fractal dimensions help
because instead of measuring every tree and branch and twig in a forest, a survey of one
tree's measurements can be used to calculate the carbon dioxide of the entire forest. To
put it simply, one tree would be measured for the amount of carbon dioxide it would
take in. From this tree, there is a distribution of different sized branches. This distribution
should match the distribution of sizes of trees in the entire forest, meaning the forest
is one enormous fractal itself.Benoit Mandelbrot was Polish-born on November 20, 1924 and was
a French Mathematician. Since he was the catalyst for the discovery of fractals, he is best
known as the Father of Fractal Geometry. He is credited with coining the name fractals
to describe objects and surfaces, which are irregular at various dimensions of scale.
It wasn't until 1975 that Mandelbrot's fractal geometry replaced Euclidian geometry, which
had dominated our mathematical thinking for thousands of years. We now know that Euclidian
geometry pertained only to the artificial realities of the first, second and third dimensions.
These dimensions are imaginary. Only the fourth dimension, which is the dimension of the space-time
continuum we live in, is real. Mandelbrot asked an excellent question: how can one determine
the length of a coastline without following the entire shore with measuring equipment?
This question, as well as other mathematical problems, began Mandelbrot's search. His
search ultimately lead to his studies on fractal dimensions, where he introduced a way of measuring
the degree of roughness or irregularity of an object. Although Mandelbrot should be credited
with the majority of the study on fractals, it was Gaston Julia's modern dynamical systems
theory that saved Mandelbrot from hours upon hours of advanced calculations. As a result,
Mandelbrot relied on computers to plot images and calculate the seemingly endless iterations.
Without this technology, it is unlikely Mandelbrot would have been able to discover as much as
he did. One unique and very famous observation made
by Mandelbrot is known as the Mandelbrot Set. This famous quadratic recurrence equation,
z = z^2 + c , is another example of a design with complex irregularities, that is self-similar
in itself, with a base shape that is similar to the image on the left below. The resulting
self-similar iteration can be as complex as the image on the right below.
Shown here are others who greatly helped with the exploration of Fractals and their contributions.
Fractals can also be found in the medical field. Application of fractal geometry to
cell biology stemmed from the discovery that cellular membrane systems had fractal properties.
Areas such as stem cell research, radiation treatment, and other uncertain cures may all
be ruled out if fractals take a bigger role in the field of medicine. The respiratory,
circulatory, and nervous systems are great examples of branches subdividing over and
over in a fractal form. Below is a cast of lungs that clearly show the symmetry or self-similarity
that every ultra-organized fractal has. It was shown that normal vasculature has a fractal
dimension of 1.7 while tumours have a fractal dimension of 1.89. Meaning, tumours are a
more chaotic vasculature, making them stand out from surrounding vasculature.Charles Darwin
was a Biologist and Scientist born February 12, 1809 in Shrewsbury, England. He is best
known for his work as a naturalist, developing the theory of evolution and the process of
natural selection. However, the question of "design" in nature troubled Darwin all
his professional life. Darwin once wrote, "I am conscious that I am in an utterly
hopeless muddle. I cannot think that the world, as we see it, is the result of chance; and
yet I cannot look at each separate thing as the result of design." Many other scientists
explained the "design" of nature as just occurring because of the creator of this world
- or God. It was said that the perfection of nature was due to arbitrariness and accident.
Darwin, however, seems to have been correct in his assumption that the world cannot be
created by accident. As mentioned before, self-similarity can be seen in many aspects
of nature, from rivers to mountains to clouds to seashells. All these aspects of nature
seem to be in chaotic forms but fractal dimensions can often describe their immense irregularities.
Fractals created a reason for design in nature, thus solving the problem Darwin had with natures
perfection. As in a shoreline, lightning's fractal dimension
is spectacularly arbitrary and irregular. Observing the main stem of electricity emanating
from the lightning, it appears to be similar to a tree trunk. Lightning can be compared
very closely to the irregularity of a tree but at a greater fractal dimension. Peacocks
are great examples of fractals in the animal kingdom. Of course, the fractals are in the
tail of these creatures. Also shown is a very famous fractal of a seashell. The perfect
pattern of the seashell is called the Fibonacci Spiral. Delicate Queen Anne's Lace also
demonstrates a fractal. This plant is really just wild carrot. It is a good example of
a floral fractal, as each blossom produces smaller iterative blooms. The image shown
was shot from underneath the plant so the iterations can be easily observed. Lastly,
there is a special type of broccoli. It is cousin to the cabbage and is a particularly
symmetrical fractal. This broccoli is called Romanescu. Of course, in addition to these
examples, there are innumerable fractals found in nature. If one were to think of the human
body, aren't arms and legs fractals also? The individual phalange of the finger separated
by joints could be considered iterations of the larger phalange before it and the largest
phalange could be seen as the iteration of the arm. This can also be observed with legs
and the toe phalanges. Paul Cezanne, a painter born January 19, 1839 in Aix-en-Provence,
France, once wrote, "Everything in nature is modeled according to the sphere, the cone,
and the cylinder. You have to learn to paint with reference to these simple shapes…"
However, when Benoit spoke of Fractals, he took a different approach by saying, "Clouds
are not spheres, mountains are not cones, coastlines are not circles, and bark is not
smooth, nor does lightning travel in a straight line." Since, the arts are often mirrored
after nature, it would not be surprising to see fractals in the art itself. Even if we
are unconscious of this fact, they are there. Also related to Fractals is computer generated
art, specifically artwork created using fractals themselves, have been made by uninformed programmers,
who use Mandelbrot's Set (z = z^2 + c) with a z value other than 0. These artworks turned
out to be hideous and are referred to as Mandelbrot Roadkill.
An artist named Jackson Pollock, born January 28, 1912 in Cody, Wyoming, unconsciously adopted
the language of nature, or fractals, to create his own artwork in a very self-similar form.
Pollock began with a canvas lying in a horizontal position, and used a continuous stream of
paint and gravity to achieve his painting. When compared to paintings such as Pollock's,
where drip trajectories were studied, the results were strikingly similar. The painting
on the left demonstrates a pendulum freely swinging. The paint lines are in a non-chaotic
form. However, the middle painting was achieved when the pendulum was knocked at a frequency
slightly lower than the one at which it naturally swings. When examining a smaller portion of
these paintings, it can be seen, that a small section has similar statistical data compared
to the entire canvas. If a person gleaned only one piece of knowledge from this paper,
it should be the fact that fractals are everywhere. Fractals make up the food we eat, the flowers
we keep in our homes, the various parts of our bodies, the artwork we observe, the décor
we use at home, the weather just outside our doors, and even the animals we keep. When
so many things in this world seem so random and chaotic, fractals make sense of the arbitrariness.
This topic is extremely new and very under-explored. More attention needs to be paid to the world
of fractals, more importance needs to be placed on learning about fractals, and more studies
need to be completed about fractals. This topic of discussion is not just some cool
mathematical element, but instead, blends mathematics with every sphere of knowledge.
From nature, to art, to medicine and beyond, fractals are showing themselves and giving
the world a new avenue to explore and from which to gain great insight. Exploring fractal
dimensions could aid in finding cures for cancer, find sanity in seemingly random paintings,
and give lucidity to beautiful aspects of nature. Clearly, this is the perfect topic
to delve into for the betterment of human understanding.
-------------------------------------------
VIDEO: Former mentor faces 215 years in prison for 11 counts of child sex abuse - Duration: 1:58.
TAX PLACE FOR INVESTMENT.
OF FORMER TULSO YOUTH
MENTOR WAS SENTENCED TODAY TO
215 YEARS IN PRISON.
52-YEAR-OLD TIMOTHY CATO HAS
BEEN FIND -- FOUND GUILTY OF
CHILD SEXUAL ABUSE.
Reporter: 215 YEARS IN
PRISON.
THE ASSISTANT DISTRICT ATTORNEY
SAYS SHE IS GLAD THE JUDGE
FOLLOWED THE JURY'S SENTENCING
RECOMMENDATION FOR THE SAKE OF
THE CHILDREN.
IT IS JUSTIFICATION FOR ALL
OF THE CHILDREN WHO CAME
FORWARD TO SPEAK FOR EVERYBODY
ELSE.
I AM DISAPPOINTED IN THE
DECISION TODAY REGARDING GIVING
CONSECUTIVE TIME INSTEAD OF
CONCURRENT TIME.
Reporter: WE TOLD YOU BACK
IN NOVEMBER THAT TIMOTHY CATO
WAS CHARGED WITH 11 COUNTS OF
CHILD SEX-ABUSE.
HE THEY SAY HE USED HIS JOB TO
PRAY ON YOUNG BOYS AND SHELTERS
THAT DID NOT HAVE A FIGURE.
HE WAS IN EVERY POSSIBLE
POSITION YOU COULD PUT YOURSELF
IN.
POLICE STARTED
INVESTIGATING BACK IN 2014 BUT
PROSECUTORS SAY THE CRIMES DATE
BACK TO 2007.
ONE BOY WAS AS YOUNG AS NINE
YEARS OLD.
THEY SAY THAT TIMOTHY CATO
MANIPULATED THEM. HE WOULD
TOUCH THEM INAPPROPRIATELY IN
THEIR SLEEP.
CHILDREN ARE TAKEN OUT OF
HOMES WHERE THERE IS VIOLENCE
OR DRUG ABUSE, AND HE TOOK HIM
INTO HIS HOME AND ABUSE THEM.
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VIDEO: Sand Springs police search for man accused of offering girl candy at bus stop - Duration: 1:28.
THE CAPITAL TONIGHT.
WE WILL HAVE HIS PRESIDENTIAL
ADDRESS STARTING AT 7:00 P.M.
TONIGHT.
A CHILD HAS BEEN APPROACHED
BY A STRANGER FOR THE SECOND
TIME IN ONE WEEK.
THIS CASE INVOLVES A MAN
OFFERING CANDY.
LET'S GO TO CAILEY DOUGHERTY
WHO IS LIVE FOR US.
Reporter: THIS LAST INCIDENT
HAPPENED AT A SCHOOL AND THIS
ONE HAPPENED OUTSIDE THESE
APARTMENTS. HERE IS A LOOK AT
THE SUV POLICE ARE LOOKING FOR.
A 13-YEAR-OLD GIRL WAS WAITING
FOR THE BUS WITH THREE OTHER
STUDENTS WHEN A RED FORD
EXPEDITION STOPPED IN THE
MIDDLE OF THE ROAD AND A 40-
YEAR-OLD MAN WITH OF BEARD
OFFERED CANDY TO THE GIRL.
SHE REFUSED TO GO OVER TO HIM.
ANY TIME A STRANGER APPROACHES
A CHILD LIKE THIS, MANY FEARED
THE WORST.
I CAN'T IMAGINE IT. I CAN'T
IMAGINE ANYONE LOSING THEIR
KIDDO.
Reporter: POLICE SAY THE DO
NOT BELIEVE THAT THESE TWO
INCIDENTS ARE CONNECTED BUT
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