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Who said math can’t be interesting? Fractals like these can seem too perfect to be true, but they occur in nature and plants all the time and are examples of math, physics, and natural selection at work!

When we see order in the world, we think it must be some human hand that made it so. But Galileo Galilei in his Il Saggiatore wrote, “[The universe] is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures.” There is order in nature, and artists who want to reproduce it faithfully spend hours studying nature’s forms.

Civilization has struggled to understand this perfect geometry for thousands of years. In the 4th century, Plato believed that symmetry in nature was proof of universal forms; in 1952, the famous code-breaker Alan Turing wrote a book trying to explain how such patterns in nature could be formed.

Now you can join in the debate. Upvote your favorite photo from the list, or upload your own!

#1

Aloe Polyphylla

Aloe Polyphylla

namraka Report

VilémRein
Community Member
9 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

Almost all of the pictures contain spirals of leaves or flowers. The spirals are mathematically described as Fibbonaci spirals and these are formed due to specific angels in which new organs are formed at the border region of the shoot apical meristem of the plant. The angle is given by the genotype and the places where are the primordia of the new organs formed are characterized by formation of a local high concentration of the plant hormone auxin. And because the plant maintains the shoot apical meristem throughout its life, there are new structures also in old plants formed in this regular shape (the only precondition is there is no damage close to the apical meristem.

Paul Walz
Community Member
9 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

NOT an aloe but an agave!!!!!!!!!!!!! Get the facts STRAIGHT!!! Dead give away sharp points on the ends of the leaves , aloes do NOT do this

DonaldHarris
Community Member
10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

Fractal repetition can be seen everywwhere in nature

nedaownu13
Community Member
10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

All of these are based off of Fibonacci numbers

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    #2

    Romanesco Broccoli

    Romanesco Broccoli

    Didier Kobi Report

    Rism
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    Whoah! Never see this in supermarket

    Colin Taylor
    Community Member
    9 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    Just the nicest Cauliflower ever(never heard it called Broccoli?)

    SuBennett
    Community Member
    9 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    Romanesco cauliflower it's called in the UK. Great flavour- There's an orange and yellow one too!

    DonaldHarris
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    NOT symmetry! fractal repetition

    DonaldHarris
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    This is NOT SYMMETRY; it is fractal repetition. Romanesco is beautiful and tasty. I used to grow it.

    SandraPrenzler
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    It's pleasing to the eye :) It's pleasing to the eye <3

    VictoriaNobes
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    I'm growing these this year - we love it but it's quite expensive in comparison to normal broccoli!

    ZacharyHarra
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    The multi colored collie flower is amazing also.

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    #3

    Crassula Buddha's Temple Plant

    Crassula Buddha's Temple Plant

    Grenville Report

    VilémRein
    Community Member
    9 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    There are no spirals, the genetically given angle of formation of new leaves is in this case exactly 90°.

    CarolCampbell
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    Where can I find this lant? This is total beautiful.

    #4

    Amazon Lily Pad

    Amazon Lily Pad

    Amazon Lily Pad

    imgkid.com Report

    Lauren Stone
    Community Member
    9 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    Awesome. Looks like a human placenta. Looks like the tree of life.

    VilémRein
    Community Member
    9 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    Also the leaf veins formation is regulated by the hormone auxin. The leaf veins form in the places where polar auxin transport channels are formed.

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    #5

    Dahlia

    Dahlia

    amazon2008 Report

    DariaB
    Community Member
    9 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    Looks like it will make sounds if I squeeze it.

    JenniferNorthFitzgibbons
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    Love the color and each little perfect section. Nature at her finest. My favorite flower! <3

    VilémRein
    Community Member
    9 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    If look carefully, you will see also the Fibbonaci spirals.

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    #6

    Flowers Like Jeweled Carpet

    Flowers Like Jeweled Carpet

    Morgan Glines Report

    MinRyan
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    Absolutely gorgeous! Look like little frosted fruit hugs bursting with flavour (probably poisonous). Would love to know what they're called?

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    #7

    Drosophyllum Lusitanicum

    Drosophyllum Lusitanicum

    ramamayoor Report

    voivod1111
    Community Member
    9 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    Portuguese? I know the Roman Latin name for Portugal was Lusitania (Hispania), l think more commonly known as 'The Portuguese Sundew'

    Janet Paulin
    Community Member
    9 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    I thought this list is about symmetry. It's looking more like Fibonacci

    NicolaCCrowe
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    Magic Mushrooms in a Magical Forest!

    BarbAnson
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    this looks like some sort of crazy confectionary this looks like some sort of crazy confectionary

    MPaulaWhelan
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    looks like a fiddle-head wearing jewellery!

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    #8

    Hoya Aldrichii

    Hoya Aldrichii

    John Tann Report

    wildandfree
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    I love to eat the nectar from flowers of Hoya!

    CarolCampbell
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    I have never seen many of these plants. They are breath-taking. Where is this one found?

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    #9

    Fractal Cabbage

    Fractal Cabbage

    Epochalypse Report

    VilémRein
    Community Member
    9 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    Very nice example of Fibbonaci spirals...

    GlynisLailann
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    Every time I cut a cabbage I always marvel at the design within.

    DonnaTolmatch
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    Ah nature. So much to learn and see.

    DickIacovello
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    This is a pattern I noticed the first time I cooked with purple cabbage, I’ve even used it in some of my aty pieces.

    EdnaRoebuckSoto
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    I love ART, Veggies, Fractals & Pi...; )

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    #10

    Sunflower

    Sunflower

    Luca Postpischl Report

    PiNeAPplES
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    Does anyone else see a faint star shape?

    VictoriaJostes
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    the Fibonacci numbers. https://en.wikipedia.org/wiki/Fermat%27s_spiral

    VictoriaJostes
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    the Fibonacci numbers - https://en.wikipedia.org/wiki/Fermat%27s_spiral

    #11

    Camelia

    Camelia

    Robbie Report

    MinRyan
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    Simply so gorgeous and so fragrant...beautiful

    VidaPenikas
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    Too bad most of these were not symmetrical.

    LorraineSutherland
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    So lovely and perfect, brilliant!! xx :)

    HannyHasquare
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    magnifique ! Magnifique / Wonderfull

    #12

    Spiraling Succulent

    Spiraling Succulent

    etsy.com Report

    VictoriaJostes
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    https://en.wikipedia.org/wiki/Fermat%27s_spiral

    BarbAnson
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    photo one has smooth edged leaves , these are spiky but I'd guess they're closely related

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    #13

    Thinking Cactus

    Thinking Cactus

    gigingir Report

    LouVarner
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    it looks like a brain to me. is that why it's called thinking cactus?

    VilémRein
    Community Member
    9 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    And this a fasciata mutation. The mutation is in a gene, that regulates the size of the meristematic zone of the shoot apical meristem. Due to the mutation the zone is not defined and any sign of symmetry is lost.

    LouVarner
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    looks like a brain to me. is that why it's called a thinking cactus?

    Anahi
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    It's really beautiful, but I can't say if looks like a brain (of course, the name) or some kind of furry snake º__º''

    Anahi
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    It's really beutiful, but I can't say if looks like a brain (of course, the name) or some kind of furry snake º__º''

    zoe_2
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    it looks like a brain :D

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    #14

    Viola Sacculus

    Viola Sacculus

    brcotte2007 Report

    VilémRein
    Community Member
    9 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    Wow, this was for me a new plant, I have never seen it before. For me a wonderful plant. Will immediately look for more info, about this miracle...

    AmyRogerson
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    Now THIS one I could definitely have. Great photos.

    zoe_2
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    These are soooo pretty

    MinRyan
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    Wow! on a mountain!...Likes it dry. The amazing things that grow in the most inhospitable places

    #15

    Ludwigia Sedioides

    Ludwigia Sedioides

    Donna Falcone Report

    JoiPfost
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    This makes me want to learn to paint. It's so beautiful!

    PeterUpton
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    Luwigia sedioides - species epithets always begin with a lower case letter. Sorry for pedantry, because the photo is beautiful!

    #16

    Lobelia

    Lobelia

    George F. Mobley Report

    Colin Taylor
    Community Member
    9 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    "One bite and the Bishop was sick" (Sir Henry at Rawlinson End)

    DennisWestler
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    One of the tall shrubby lobelias. like Lobelia tupa. Not at all like the sprawling bedding plants.

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    #17

    Succulents

    Succulents

    Jolina Report

    SherBear
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    Looks like Hens & Chicks.

    MinRyan
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    Love these...in that cool blue <3

    DerpzQueen
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    They come back so if you plant it once it will come back ت

    TollTolladay
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    House leek. Easy peasy to grow!

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    #18

    Pelecyphora Aselliformis

    Pelecyphora Aselliformis

    Peter Hunter Report

    MelihYalciner
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    Welche name hat diese schöne Pflanze?

    ColsonBaker
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    Es ist ein Kaktus genannt Peyotillo (ausgesprachen pejo tijo).

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    chachkimooch
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    This is cool, looks kinda like stretched out sow bugs...

    #19

    Chameleon Tail

    Chameleon Tail

    Popumon Tih Report

    DickIacovello
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    Is this a plant or real chameleon tail?

    joms
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    i think its chameleons eyes also

    CarolCampbell
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    I have never seen this one either

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    #20

    Leaf Ladder

    Leaf Ladder

    Janet Little Report

    AnitaAntolkovic
    Community Member
    9 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    This is absolutely stunning and in the same time so simple. Jeremy Narby wrote a great book about the greatness of nature: https://www.goodreads.com/work/quotes/985969-the-cosmic-serpent

    IngeLeGore
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    Totally amazing. Now I will enjoy looking for more :)

    OLdiseño
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    Reminds me of the bat wings!! Amazing Nature!

    Jacqui Parsons
    Community Member
    8 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    God is the ultimate 3D fractal artist

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    #21

    Hoya Pubicalyx

    Hoya Pubicalyx

    Botanical Wonderland Report

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    #22

    Alstroemeria Pelegrina

    Alstroemeria Pelegrina

    Florencia & Juan Report

    17_csimpson
    Community Member
    9 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    Cool I can't believe this. ITS A MIRACLE!!!!!

    #23

    Hoya Kerrii

    Hoya Kerrii

    Sandra Report

    Rcatheron
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    Looks like sugar icing flowers on a cake!

    AmyRogerson
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    I was just thinking that same thing. Beautiful cupcakes. I was just thinking that same thing. Perfect little cupcakes.

    #24

    Spiral Begonia

    Spiral Begonia

    elsewhereincuenca2.blogspot.com Report

    MaryAliceLynch
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    I have neve seen a begonia like this. It is beautiful.

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    #25

    Aeonium Tabuliforme

    Aeonium Tabuliforme

    David Szalay Report

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    #26

    Fractal Cabbage

    Fractal Cabbage

    lumiparta Report

    #27

    Echinacea

    Echinacea

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    #28

    Symetric Flowers

    Symetric Flowers

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    #30

    Pinecone

    Pinecone

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    Dragons Exist
    Community Member
    1 year ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    I've always liked pinecones when they're brown but before they open up

    #31

    Fearful Symmetry

    Fearful Symmetry

    500px.com Report

    MaryAliceLynch
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    I love the colors and the symetry. I like this one the best so far.

    #32

    Agave~tequila Plant

    Agave~tequila Plant

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    MerryMarjie
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    Ah, my favorite plant, in terms of productivity!

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    #33

    Silversword

    Silversword

    500px.com Report

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    #34

    Agave Angustifolia

    Agave Angustifolia

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    #35

    Planta Mosaico - Ludwigia Sedioides

    Planta Mosaico - Ludwigia Sedioides

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    #36

    Gerbera

    Gerbera

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    #37

    Purple Fractal Cabbage

    Purple Fractal Cabbage

    media.bridgesandballoons.com Report

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    #38

    B&w Dahlia

    B&w Dahlia

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    #39

    Unfurling Tree Fern Frond, Madeira

    Unfurling Tree Fern Frond, Madeira

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    #40

    Monstera Fruit

    Monstera Fruit

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    #41

    Araucaria Arucana

    Araucaria Arucana

    www.flickr.com Report

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    #42

    (another) Sunflover Mandala

    (another) Sunflover Mandala

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    #43

    Colorful Cacti

    Colorful Cacti

    susanbaileyphoto.com Report

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    #45

    Mandala

    Mandala

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    #46

    Mimosa

    Mimosa

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    #47

    Pinecone

    Pinecone

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    #49

    Detail Of A Fern

    Detail Of A Fern

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    #52

    Suculent

    Suculent

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    TravinMcKain
    Community Member
    9 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    This is Dudleya pulverulenta “Chalk Liveforever”

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    #53

    Water Forget-me-not

    Water Forget-me-not

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    #54

    Protier

    Protier

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    #55

    King Protea - Maui

    King Protea - Maui

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    chachkimooch
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    WOW! Now that's an impressive flower!

    #56

    Geometric Leave.

    Geometric Leave.

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    #57

    Magnolia

    Magnolia

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    #58

    Name?

    Name?

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    CaroDose
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    Looks like a chrysanthemum to me. Probably in a flower show since it's a day or so past prime.

    #59

    Arjareka Gibson- 7th Period

    Arjareka Gibson- 7th Period

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    #60

    Oriental Lily

    Oriental Lily

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    #61

    Spiney Cactus

    Spiney Cactus

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    #62

    White Malaysian Mums

    White Malaysian Mums

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    #63

    Pine Candle

    Pine Candle

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    #64

    Phillip Nguyen Pd.3

    Phillip Nguyen Pd.3

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    #65

    Fractal Broccoli

    Fractal Broccoli

    en.wikipedia.org Report

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    #66

    Farjana Kshuhboo

    Farjana Kshuhboo

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    #67

    Farjana Kshuhboo P3

    Farjana Kshuhboo P3

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    #68

    Andrew Bagwell 3rd

    Andrew Bagwell 3rd

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    #69

    Camelia

    Camelia

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    #70

    Barrel Cactus

    Barrel Cactus

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    #71

    Apple Core Cross Section

    Apple Core Cross Section

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    #72

    A Strange Flower

    A Strange Flower

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    #73

    Moss On The Cobble Stones

    Moss On The Cobble Stones

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    #74

    Fuzzy

    Fuzzy

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    #76

    Maria Iniguez

    Maria Iniguez

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    #77

    Thissle

    Thissle

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    #78

    Perception By Malinda Ratliff

    Perception By Malinda Ratliff

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    #79

    Nymphalis Antiopa Butterfly

    Nymphalis Antiopa Butterfly

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    #80

    Camelia2

    Camelia2

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    #82

    Water Lily, Shot At Gutty Meusium.

    Water Lily, Shot At Gutty Meusium.

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    #83

    Geometric Flower.

    Geometric Flower.

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    KathiePhelps
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    That's a Clematis of some variety

    #84

    Little Star

    Little Star

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    #85

    Lilac

    Lilac

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    #86

    Black Hollyhock

    Black Hollyhock

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    #87

    Flower

    Flower

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    #88

    Common Dandelion

    Common Dandelion

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    #90

    Rose From Ariana

    Rose From Ariana

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    #91

    Phillip Nguyen Pd3 Got Emm

    Phillip Nguyen Pd3 Got Emm

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    #92

    Young Lily Before Blooming

    Young Lily Before Blooming

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    #93

    Maria Iniguez

    Maria Iniguez

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    #94

    Heal All

    Heal All

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    #95

    Thistle

    Thistle

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    #96

    Colorado Columbine

    Colorado Columbine

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    #97

    Columbine

    Columbine

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    #98

    King Protea - Maui

    King Protea - Maui

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    #99

    Geometric Leave.

    Geometric Leave.

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    #100

    Nature At Its Best

    Nature At Its Best

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    #101

    Sunflower

    Sunflower

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    #102

    Tulip

    Tulip

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    #103

    A Bruce, - Following The Sun's Path ?

    A Bruce, - Following The Sun's Path ?

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    #104

    From My Garden

    From My Garden

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    #105

    Sunflower

    Sunflower

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    #106

    Colorado Columbine

    Colorado Columbine

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    #107

    Purple

    Purple

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    JosieSchmitz
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    Some variety of Dahlia I'm guessing

    #108

    Mums

    Mums

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    #109

    Phillip Nguyen Period 3

    Phillip Nguyen Period 3

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    KiaL
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    #youGuessedIt #YouWasWrong

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    #110

    Fibonacci Music By: Alexis Hernandez

    Fibonacci Music By: Alexis Hernandez

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    KiaL
    Community Member
    10 years ago Created by potrace 1.15, written by Peter Selinger 2001-2017

    I think this has absolutely nothing to do with the article!! #YouGuessedIT #YouWasWrong

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    #111

    Iparanas's Symmetry

    Iparanas's Symmetry

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    #112

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