How to Acquire and Logically Perceive the Rose Curve

Step-by-Step Guide

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   Step 1: Open Excel by clicking on the green X icon on the dock

   Select from the File menu, Open New Worksheet.
   
   Save the file as "Rose Curve" or something similar into a logical filer folder like "LifeGuide Hub articles" or "MS XL Imagery". or something similar.
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   Step 2: or by opening it from within the Microsoft folder in your Applications folder by double-clicking on it.

   ,,, Do Insert Name Define n for the selection.
   
   Format cells fill Light Blue.
   
   Enter to cell J3, 1, and select range J3:
   J11 and Edit Fill Series (step value = 1). so that J11 ends up with 9 in it.
   
   Do Insert Name Define d for the selection.
   
   Format cells fill Light Brown.
   
   Edit Go to cell range K3:
   Q11 and enter to K3 the formula, w/o quotes, "=n/d"
   
   and Edit Fill Down and Edit Fill Right.
   
   The formula should be active and return the value 1 (in a diagonal to the lower right).
   
   Select cell N4 and Format cells Fill Yellow and Insert Name Define Selector to cell $N$4, with the Sheet Name and exclamation point preceding it, OK. , Edit Go to cell range I3:
   I3601, enter w/o quotes "=k" in cell I3 and Do Edit Fill Down. , This has the effect of scaling the chart larger or smaller on the axes scales, without changing the form of the chart.,,, So why not just put in k instead? Because this way, you can vary the constant k in various ways and make some clever designs of your own.
   
   Edit Go To cell range A2:
   D90 and do Edit Fill Down.
   
   Only 90 data points are required for the simple charts to be.
   
   Edit Go To cell range E2:
   F3601 and do Edit Fill Down.
   
   There may be some data series line overlay on some charts but 10*360 data points should take care of most creative ideas. , Cut it and paste it under the n/d data box.
   
   Click on the data series in the plot of the chart and edit the series in the Formula Bar to read as follows: "=SERIES("Rose Figure"
   
   Sheet2!$E$2:$E$3602,Sheet2!$F$2:$F$3602,1)"
   
   without external quotes.
   
   Whether or not you add a picture under your data is up to you of course
   -- to do so, click in the absolute upper leftmost box between Column A and Row 1 to select the entire sheet and do Format Sheet Background and select a .png or .jpg file for your sheet's background.
   
   Use the Grab application if working on a Mac to take a partial screen shot, copy it, open New file from Clipboard in the Preview app, and export the file as a .png or .jpg file, or do Edit Copy Picture and copy picture and go to the Saves worksheet tab and do Edit Paste Picture.
   
   Include the k setting and which n/d was selected, and if you've changed a formula, select on that to get it in the formula bar within your picture frame. , Edit the chart series to read, w/o external quotes, "=SERIES("Cos, Sin Chart"
   
   Sheet2!$A$2:$A$90,Sheet2!$B$2:$B$90,1)".
   
   Position the chart under and to the left of the Main Chart, shrinking it with the grab handle at lower right by hovering over the corner until a double-headed arrow appears and then grabbing the lower right hand corner and adjusting diagonally. cos(t)*sin(t)=x, cos(t)*cos(t)=y Chart:
   Select cell range C2:
   D90 and create that chart as you did above.
   
   Edit the chart series to read, w/o external quotes, "=SERIES("Cos*Cos, Cos*Sin Chart"
   
   Sheet2!$C$2:$C$90,Sheet2!$D$2:$D$90,1)".
   
   Position the chart under and to the right of the Main Chart, shrinking it with the grab handle at lower right by hovering over the corner until a double-headed arrow appears and then grabbing the lower right hand corner and adjusting diagonally.
   
   Your charts should resemble this grabbed and Preview-exported jpg: , There are certainly resemblances to floral limiting forms among those in the diagram.
   
   By "limiting forms"
   
   what is meant is that flowers probably grow according to phyllotaxis and Phi, and are generated by iterative fractal formulas growing both larger and more detailed as edges are approached, but that the overall limiting forms of many flowers resemble these trigonometric images.
   
   Math and computer simulations are coming closer and closer to true-to-life imagery based on 1) the knowledge of how plants actually grow, and 2) keener mathematical modeling of the growth processes.
   
   You may want to study more about "phyllotaxis" if this interests you, or if closest packing does.
   
   To make the image to the right of the k=n/d data table showing the various rose forms it generates, substitute into cell H1 the term ConstantRadius and Insert Define Name ConstantRadius to cell H2, and input the value 6 to cell H2.
   
   Then enter to cell E2 without quotes, the formula, "=(COS(I2*G2*PI()/180)*SIN(G2*PI()/180))-(COS(ConstantRadius*G2*PI()/180)*SIN(G2*PI()/180))" Then enter to cell F2 without quotes, the formula, "=(COS(I2*G2*PI()/180)*COS(G2*PI()/180))-(COS(ConstantRadius*G2*PI()/180)*COS(G2*PI()/180))" Edit Go To cell range E2:
   F3661 and do Edit Fill Down.
   
   This formula adaption creates inner bud petals which are more realistic of some actual roses and flowers. k has been set to "=Q10"
   
   w/o quotes.
   
   Q10 has yellow fill.
   
   Formatting of the colorful chart on right:
   Line is smoothed, 0% transparency, 1 pt., firetruck red.
   
   Glow is firetruck red, 30 pt size, 50% transparent, soft edges are 0 pt.
   -- it is because of the "inner petals" that the glow seems to pertain to the entire petals, with no show-through of the plot area formatting.
   
   There's no market style (no markers).
   
   There's no Shadow.
   
   Plot Area:
   Fill is Gradient Radial Centered 43% Exxon blue, 100% canary yellow; no Glow, no Shadow, no 3D Format, Line = Automatic.
   
   This file was moved to a new worksheet and retitled Rose3.xlsx , PI()/180 converts from radians to degrees (the default is radians, or 180/PI()).
   
   Chart the series after doing Edit Fill down in cell range E2:
   F3661.
   
   Your chart should resemble the following:
   The formatting for this chart is Glow 30pt, Transparency 57%, Soft Edges 0 pt, in Red. , Then close your eyes.
   
   What do you see? The mind has stored within in it Ideals/Models of what geometric patterns flowers most resemble.
   
   How does the mind do this? Does it calculate them? Does it remember them from various art designs? Or are they hard-wired deep in our DNA? , While none of these patterns are 3D and not that realistic therefore, we recognize them anyway.
   
   That is another key point: that we are able to translate for 3 dimensions to 2 rapidly should tell us we have a focusing/filtering method that can strip away unnecessary detail., For example, large petals and flowers will attract pollinators at a large distance and/or that are large themselves.
   
   Collectively the scent, color and shape of petals all play a role in attracting/repelling specific pollinators and providing suitable conditions for pollinating.
   
   Some pollinators include insects, birds, bats and the wind., That sort of Pattern Creation in human imagination is what makes for tool-making, design work of all kinds, role play, etc.
   
   It's part of Nature finding new niches for Life to exist in possibly.
   
   Above is a flower that was generated that looks nothing like any other flower., ConstantRadius was then set to .95,,,,, Some background shows through.
   
   The idea of partially transparent flowers was appealing.,,,, Various pollinators prefer or dislike various plants, and have developed various coping strategies, one of which is the general shape of the flower, another is the number of petals and yet another is the size of each petal.
   
   This point generally does not apply for reliance on the wind to provide pollination, except the stamen(s) require exposure, and likewise for the female receptor organ(s).
   
   Plants can seem to be very preferential in the pollination species/method they "employ"
   
   as has evolved for their niche over time in a vast array of choices for the pollinators.,, Plants evolve to be therefore "competitive" viewed one way, or "in harmony" with all the other variations in their environment.,, by being a "mutant".
   
   It may find a way to "mute" another species' popularity., One of the ways we do this is by the pattern we perceive the plant has as compared with other plants.
   
   Over time, we have come to know certain plants are friendly or harmful to our visual, digestive, olfactory, tactile and other senses.,, the curves of the plant's various parts, especially its leaves and petals., It is an area that deserves more study and focused effort, now that we have the advantage of large number-crunching computers and methods such as Bézier Curve theory.
   
   Please see the article How to Acquire Bézier Curves Using Excel.,, For more art charts and graphs, you might also want to click on Category:
   Microsoft Excel Imagery, Category:
   Mathematics, Category:
   Spreadsheets or Category:
   Graphics to view many Excel worksheets and charts where Trigonometry, Geometry and Calculus have been turned into Art, or simply click on the category as appears in the upper right white portion of this page, or at the bottom left of the page.
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   Step 3: Set Preferences Be mindful that these settings will affect your future XL work; General - Set Show this number of recent documents to 15; set Sheets in new workbook to 3; this editor works with Body Font

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   Step 4: in a font size of 12; set your preferred file path/ location; View - Check Show formula bar by default; check Indicators only

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   Step 5: and comments on hover for Comments; show All for objects; Show row and column headings

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   Step 6: Show outline symbols

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   Step 7: Show zero values

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   Step 8: Show horizontal scroll bar

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   Step 9: Show vertical scroll bar

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    Step 10: Show sheet tabs; Edit - Check all; Display 0 number of decimal places; set Interpret as 21st century for two-digit years before 30; Uncheck Automatically convert date system; AutoCorrect - Check all Chart - In Chart Screen Tips

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    Step 11: check Show chart names on hover

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    Step 12: and check Show data marker values on hover; leave the rest unchecked; Calculation - Automatically checked; Limit iteration to 100 Maximum iterations with a maximum change of 0.0001

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    Step 13: unless goal seeking

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    Step 14: then .000 000 000 000 01 (w/o spaces); check Save external link values; Error checking - Check all and this editor uses dark green or red to flag errors; Save - Check all; set Automatic Save to 5 minutes; Compatibility - check Check documents for compatibility Ribbon - All checked

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    Step 15: except Hide group titles is unchecked.

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    Step 16: By double-clicking on the bottom worksheet tabs

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    Step 17: make the left first tab label Data and the second one to the right Saves (for copied picture of your charts and data settings so that you may recreate patterns)).

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    Step 18: Add Row 1 and 2 column headers: Enter to cell A1 cos (t) Enter to cell B1

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    Step 19: sin(t) Enter to cell C1

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    Step 20: cos(t)*sin(t) Enter to cell D1

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    Step 21: cos(t)*cos(t) Enter to cell E1

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    Step 22: x=cos(kt)*sin(t) Enter to cell F1

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    Step 23: y=cos(kt)*cos(t) Enter to cell G1

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    Step 24: t Enter to cell H1

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    Step 25: Proportioner Enter to cell I1

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    Step 26: k=n/d Enter to cell K1

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    Step 27: n Enter to cell J2

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    Step 28: Fill in the n/d Table: Enter to cell K2

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    Step 29: and select range K2:Q2 and Edit Fill Series (increment or step value = 1)

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    Step 30: so that Q2 ends up with 7 in it.

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    Step 31: Enter k=n/d (numerator/denominator) column Defined Name variable and data Select cell I2 and do Insert Name Define name k to the cell; Select cell I2 and enter w/o quotes the formula "=Selector" and Format Cell Fill yellow.

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    Step 32: Proportioner: Select cell H2 and enter 10.

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    Step 33: t: Edit Go To cell range G2:G3601 and input 0 to cell G2 and do Edit Fill Series (with Step Value = 1).

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    Step 34: Fill in the cos

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    Step 35: x and y formulas: Enter to cell A2

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    Step 36: w/o quotes

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    Step 37: the formula

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    Step 38: "=cos(G2)" Enter to cell B2

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    Step 39: w/o quotes

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    Step 40: the formula

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    Step 41: "=sin(G2)" Enter to cell C2

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    Step 42: w/o quotes

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    Step 43: the formula

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    Step 44: "=A2*B2" Enter to cell D2

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    Step 45: w/o quotes

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    Step 46: the formula

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    Step 47: "=A2*A2" Enter to cell E2

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    Step 48: w/o quotes

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    Step 49: the formula

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    Step 50: "=Proportioner*COS(I2*G2*PI()/180)*SIN(G2*PI()/180)"

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    Step 51: Enter to cell F2

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    Step 52: w/o quotes

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    Step 53: the formula

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    Step 54: "=Proportioner*COS(I2*G2*PI()/180)*COS(G2*PI()/180)" and notice that I2 will change to I3 and I4 etc as we fill the formulas down.

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    Step 55: Main Chart Stay in or Edit Go To cell range E2:F3601 and from the Ribbon or Menu

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    Step 56: select Chart

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    Step 57: Scatter

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    Step 58: Smoothed Line Scatter -- a chart should appear on your sheet.

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    Step 59: Simple Circle Chart To see the simple situation of cos and sin being charted as {x

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    Step 60: select cell range A2:B90 and create that chart as you did above.

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    Step 61: Check this file on what the entire of the 7x9 k=n/d box produces

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    Step 62: plus a chart this editor-author made using formula adaptations.

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    Step 63: Simpler formula: Enter to cell E2 w/o quotes the formula

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    Step 64: "=(COS(I2*G2*PI()/180)*SIN(G2*PI()/180))" and Enter to cell F2 w/o quotes the formula

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    Step 65: "=(COS(I2*G2*PI()/180)*COS(G2*PI()/180))"

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    Step 66: where I2:I3661 = k and G2:G3661 = t series from 1 to 3600.

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    Step 67: Look again at the chart of the rose patterns.

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    Step 68: The key to the answer lies in the fact that Nature herself uses these as Limiting Forms of various plants -- the same type of plant generally has the same type of pattern.

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    Step 69: The shape and size of the flower/petals is important in selecting the type of pollinators they need.

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    Step 70: Suppose instead that one wants to add detail and be creative -- make flowers that are unique art creations

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    Step 71: Logically

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    Step 72: one will start with a known pattern and then deviate from it along the way because one wants basic likeness and detailed differentiation.

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    Step 73: It was done by setting k - n/d = 15/1 as the table was first expanded rightwards.

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    Step 74: The formula used in E2 was "=(COS(I2*G2*PI()/180)*SIN(G2*PI()/180))-(COS(ConstantRadius*G2*PI()/180)*SIN(G2*PI()/180))" and

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    Step 75: The formula used in F2 was "=(COS(I2*G2*PI()/180)*COS(G2*PI()/180))-(COS(ConstantRadius*G2*PI()/180)*COS(G2*PI()/180))

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    Step 76: which was then

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    Step 77: Edit Fill Down to E2:F3661

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    Step 78: and create the chart

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    Step 79: adding unique effects.

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    Step 80: Observe that the petals are parabolic at their tip but then meet at the center due to needing 15 of them

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    Step 81: and they have repetitious petals near their outer ends due to the .95 k setting.

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    Step 82: Use data markers.

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    Step 83: You were shown above the simpler charts of a circle and one with waves bordering it.

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    Step 84: Think of sine and cosine as being capable of producing circles

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    Step 85: waveforms

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    Step 86: cycling forms and curves.

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    Step 87: By multiplying by an increment like t

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    Step 88: the sine or cosine function

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    Step 89: with results between 1 and -1

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    Step 90: increments and decrements in an orderly manner.

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    Step 91: Observe that Nature is conservative with resources yet quite expansive in production of biodiversity -- Nature tries many possibilities

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    Step 92: so her "use" of ratios when the numerator/denominator varies within integers that are simple and less than 10 generally

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    Step 93: and produces fairly simple patterns.

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    Step 94: Perceive that various shapes may be more appealing than others to specific pollinators.

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    Step 95: Perceive that these shapes and their number are in the minority

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    Step 96: generally speaking

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    Step 97: out of all the flowering species in an a given area.

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    Step 98: Perceive that a plant that has a "new formula" may attract interest it might not otherwise

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    Step 99: as likeness is not particularly "competitive"

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     Step 100: or in a unique harmonious position

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     Step 101: whichever way one chooses to look at the situation.

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     Step 102: somewhere in the DNA is a "creative element" that can try new "formulations" of shape

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     Step 103: number

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     Step 104: These genetic alterations are divisible into groups and individuals by humans

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     Step 105: who typify plants into genera and classes and families

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     Step 106: We start with the simple and move to the complex -- thus

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     Step 107: the 3-leaved plants are known better than obscure species where the sepals are barely separable from the petals in form and/or function.

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     Step 108: One of the ways we collect into groups is by analyzing the shapes

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     Step 109: Curve Analysis is a difficult discipline.

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     Step 110: Final Image:

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     Step 111: Make use of helper articles when proceeding through this tutorial: See the article How to Create a Spirallic Spin Particle Path or Necklace Form or Spherical Border for a list of articles related to Excel

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     Step 112: Geometric and/or Trigonometric Art

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     Step 113: Charting/Diagramming and Algebraic Formulation.

Detailed Guide

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