How to Acquire and Logically Perceive the Rose Curve

Six Parts:The TutorialCreate the ChartsRose FormsLogical PerceptionMath and Perception; Nature Observing HerselfHelpful Guidance

One of the keys to creative intelligence is perception of pattern(s). In this article, you'll learn to create the Rose Curve (or pattern or form) and two different formulas for it, and reason through the formulas to see something of the why and how one recognizes this familiar pattern-set.


  • Become familiar with basic image to create:

Part 1
The Tutorial

  1. 1
    Open Excel by clicking on the green X icon on the dock, or by opening it from within the Microsoft folder in your Applications folder by double-clicking on it.
    • Select from the File menu, Open New Worksheet.
    • Save the file as "Rose Curve" or something similar into a logical filer folder like "wikiHow articles" or "MS XL Imagery". or something similar.
  2. 2
    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, in a font size of 12; set your preferred file path/ location;
    • View - Check Show formula bar by default; check Indicators only, and comments on hover for Comments; show All for objects; Show row and column headings, Show outline symbols, Show zero values, Show horizontal scroll bar, Show vertical scroll bar, 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, check Show chart names on hover, 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, unless goal seeking, 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, except Hide group titles is unchecked.
  3. 3
    By double-clicking on the bottom worksheet tabs, 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)).
  4. 4
    Add Row 1 and 2 column headers:
    • Enter to cell A1 cos (t)
    • Enter to cell B1, sin(t)
    • Enter to cell C1, cos(t)*sin(t)
    • Enter to cell D1, cos(t)*cos(t)
    • Enter to cell E1, x=cos(kt)*sin(t)
    • Enter to cell F1, y=cos(kt)*cos(t)
    • Enter to cell G1, t
    • Enter to cell H1, Proportioner
    • Enter to cell I1, k=n/d
    • Enter to cell K1, n
    • Enter to cell J2, d
  5. 5
    Fill in the n/d Table:
    • Enter to cell K2, 1, and select range K2:Q2 and Edit Fill Series (increment or step value = 1), so that Q2 ends up with 7 in 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.
  6. 6
    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.
    • Edit Go to cell range I3:I3601, enter w/o quotes "=k" in cell I3 and Do Edit Fill Down.
  7. 7
    Proportioner: Select cell H2 and enter 10. This has the effect of scaling the chart larger or smaller on the axes scales, without changing the form of the chart.
  8. 8
    t: Edit Go To cell range G2:G3601 and input 0 to cell G2 and do Edit Fill Series (with Step Value = 1).
  9. 9
    Fill in the cos, sin, x and y formulas:
    • Enter to cell A2, w/o quotes, the formula, "=cos(G2)"
    • Enter to cell B2, w/o quotes, the formula, "=sin(G2)"
    • Enter to cell C2, w/o quotes, the formula, "=A2*B2"
    • Enter to cell D2, w/o quotes, the formula, "=A2*A2"
    • Enter to cell E2, w/o quotes, the formula, "=Proportioner*COS(I2*G2*PI()/180)*SIN(G2*PI()/180)"
  10. 10
    Enter to cell F2, w/o quotes, the formula, "=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. 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.

Part 2
Create the Charts

  1. 1
    Main Chart
    • Stay in or Edit Go To cell range E2:F3601 and from the Ribbon or Menu, select Chart, All, Scatter, Smoothed Line Scatter -- a chart should appear on your sheet. 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$3602,1)", without external quotes. Whether or not you add a picture under your data is up to you of course -- to do so, click in the absolute upper leftmost box between Column A and Row 1 to select the entire sheet and do Format Sheet Background and select a .png or .jpg file for your sheet's background.
    • Use the Grab application if working on a Mac to take a partial screen shot, copy it, open New file from Clipboard in the Preview app, and export the file as a .png or .jpg file, or do Edit Copy Picture and copy picture and go to the Saves worksheet tab and do Edit Paste Picture. Include the k setting and which n/d was selected, and if you've changed a formula, select on that to get it in the formula bar within your picture frame.
  2. 2
    Simple Circle Chart
    • To see the simple situation of cos and sin being charted as {x, y}, select cell range A2:B90 and create that chart as you did above. Edit the chart series to read, w/o external quotes, "=SERIES("Cos, Sin Chart",Sheet2!$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:

Part 3
Rose Forms

  1. 1
    Check this file on what the entire of the 7x9 k=n/d box produces, plus a chart this editor-author made using formula adaptations. 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
  2. 2
    Simpler formula:
    • Enter to cell E2 w/o quotes the formula, "=(COS(I2*G2*PI()/180)*SIN(G2*PI()/180))" and
    • Enter to cell F2 w/o quotes the formula, "=(COS(I2*G2*PI()/180)*COS(G2*PI()/180))", where I2:I3661 = k and G2:G3661 = t series from 1 to 3600. 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.

Part 4
Logical Perception

  1. 1
    Look again at the chart of the rose patterns. 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?
  2. 2
    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. 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.
  3. 3
    The shape and size of the flower/petals is important in selecting the type of pollinators they need. 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.
  4. 4

    Suppose instead that one wants to add detail and be creative -- make flowers that are unique art creations, Logically, one will start with a known pattern and then deviate from it along the way because one wants basic likeness and detailed differentiation.
    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.
  5. 5
    It was done by setting k - n/d = 15/1 as the table was first expanded rightwards. ConstantRadius was then set to .95
  6. 6
    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
  7. 7
    The formula used in F2 was "=(COS(I2*G2*PI()/180)*COS(G2*PI()/180))-(COS(ConstantRadius*G2*PI()/180)*COS(G2*PI()/180)), which was then
  8. 8
    Edit Fill Down to E2:F3661, and create the chart, adding unique effects.
  9. 9
    Observe that the petals are parabolic at their tip but then meet at the center due to needing 15 of them, and they have repetitious petals near their outer ends due to the .95 k setting.
  10. 10
    Use data markers. Some background shows through. The idea of partially transparent flowers was appealing.

Part 5
Math and Perception; Nature Observing Herself

  1. 1
    You were shown above the simpler charts of a circle and one with waves bordering it.
  2. 2
    Think of sine and cosine as being capable of producing circles, waveforms, cycling forms and curves.
  3. 3
    By multiplying by an increment like t, the sine or cosine function, with results between 1 and -1, increments and decrements in an orderly manner.
  4. 4
    Observe that Nature is conservative with resources yet quite expansive in production of biodiversity -- Nature tries many possibilities, so her "use" of ratios when the numerator/denominator varies within integers that are simple and less than 10 generally, and produces fairly simple patterns. 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.
  5. 5
    Perceive that various shapes may be more appealing than others to specific pollinators.
  6. 6
    Perceive that these shapes and their number are in the minority, generally speaking, out of all the flowering species in an a given area. Plants evolve to be therefore "competitive" viewed one way, or "in harmony" with all the other variations in their environment.
  7. 7
    Perceive that a plant that has a "new formula" may attract interest it might not otherwise, as likeness is not particularly "competitive", or in a unique harmonious position, whichever way one chooses to look at the situation.
  8. 8
    So, somewhere in the DNA is a "creative element" that can try new "formulations" of shape, number, color, etc. by being a "mutant". It may find a way to "mute" another species' popularity.
  9. 9
    These genetic alterations are divisible into groups and individuals by humans, who typify plants into genera and classes and families, etc. 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.
  10. 10
    We start with the simple and move to the complex -- thus, the 3-leaved plants are known better than obscure species where the sepals are barely separable from the petals in form and/or function.
  11. 11
    One of the ways we collect into groups is by analyzing the shapes, i.e. the curves of the plant's various parts, especially its leaves and petals.
  12. 12
    Curve Analysis is a difficult discipline. 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.
  13. 13
    Final Image:

Part 6
Helpful Guidance

  1. 1
    Make use of helper articles when proceeding through this tutorial:

Article Info

Categories: Microsoft Excel Imagery | Graphics