# Sunflower 3D

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### WHAT IS IT?

This is a 3D version of the Sunflower model in the NetLogo Models Library. The interlocking spirals found in the seeds, petals and even branches of many plants occur naturally through the growth of the flower. This model attempts to demonstrate the growth of these naturally occurring spirals.

When a new seed emerges, the older ones grow slightly and move further from the center--the source--and the youngest seed finds the largest gap between existing seeds, in which it can grow. This gap can be found by turning counter clockwise. The angle made by this turn is a multiple of the golden ratio (1.618). The golden ratio, based on the Fibonacci series (1, 1, 2, 3, 5, 8, 13...), equals the limit of F(n)/F(n-1). Thus, these spirals can be mathematically generated, using the golden ratio.

### HOW IT WORKS

For each clock-tick, a new turtle (can be seen as a seed or a petal) is created. As in nature, the turtle finds the appropriate position and begins growing. The 'appropriate position' is defined as the number of clock-ticks times the 'turn increment'. All of the other existing turtles move forward and grow slightly, with each clock-tick. If a turtle gets too close to the edge of the world, it dies.

### HOW TO USE IT

The NUM-COLORS slider controls how many colors the turtles can be. (Using this will make some of the spirals stand out more, other stand out less.)

The STEP-SIZE slider controls how far away the turtle moves from the center, for each clock-tick.

The TURN-INCREMENT slider dictates the degree that each new turtle will turn to set its position in the spiral.

The SET TURN-INCREMENT buttons help to set the TURN-INCREMENT slider to specific values at and around the golden number. They are simply there to help achieve precision that can be difficult with the slider.

You can select different shapes using the FLOWER-TYPE chooser. For each shape the turtles move in different planes. In 2D-HORIZONTAL the turtles only move in the xy-plane, in 2D-VERTICAL they move in the yz-plane and they move in all three dimensions in both PINE CONE and SPIRAL.

If ROLL? is true turtles also rotate roll by TURN-INCREMENT.

### THINGS TO NOTICE

Think about the spirals that you see. How many different ways can you make a pattern of spirals?

### THINGS TO TRY

How does adding colors change the spirals you see? Does this change the phenomena, or only what you see?

### EXTENDING THE MODEL

Make the spirals go counter-clockwise.

Make the model draw your favorite flower's petal or seed pattern. For example, a buttercup or columbine could be made by creating 5 large petals of the appropriate colors.

In nature, real plants don't have the golden number "programmed" into them. Rather, the spirals form as the result of an emergent process, described in Conway and Guy's book (see below) and other sources. Can you extend this model to capture this emergent process?

### NETLOGO FEATURES

Note in the code that the turtles "die" when the reach the edge of the world. This is so that they don't wrap around and re-appear on the opposite side.

### CREDITS AND REFERENCES

This is based on pp. 113-24 of John H. Conway and Richard K. Guy's "The Book of Numbers".

### HOW TO CITE

If you mention this model in an academic publication, we ask that you include these citations for the model itself and for the NetLogo software:

- Wilensky, U. (2003). NetLogo Sunflower 3D model. http://ccl.northwestern.edu/netlogo/models/Sunflower3D. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

- Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

In other publications, please use:

- Copyright 2003 Uri Wilensky. All rights reserved. See http://ccl.northwestern.edu/netlogo/models/Sunflower3D for terms of use.

### COPYRIGHT NOTICE

Copyright 2003 Uri Wilensky. All rights reserved.

Permission to use, modify or redistribute this model is hereby granted, provided that both of the following requirements are followed:

a) this copyright notice is included.

b) this model will not be redistributed for profit without permission from Uri Wilensky. Contact Uri Wilensky for appropriate licenses for redistribution for profit.

This is a 3D version of the 2D model Sunflower.

This model was created as part of the projects: PARTICIPATORY SIMULATIONS: NETWORK-BASED DESIGN FOR SYSTEMS LEARNING IN CLASSROOMS and/or INTEGRATED SIMULATION AND MODELING ENVIRONMENT. The project gratefully acknowledges the support of the National Science Foundation (REPP & ROLE programs) -- grant numbers REC #9814682 and REC-0126227.

## Comments and Questions

;; setup is called once at the beginning of each run ;; it clears the screen and resets the clock to setup ca end ;; hatch a new turtle and set its color and direction. ;; then each turtle moves forward by step-size, increases ;; its size and if it is on the edge of the screen, dies. to go cro 1 [ set color 10 * (ticks mod num-colors) + 15 set size 0.6 * sqrt distancexyz 0 0 0 if flower-type = "2D Horizontal" [ rt ticks * turn-increment * 360 ] if flower-type = "2D Vertical" [ tilt-up ticks * turn-increment * 360 ] if flower-type = "Pine Cone" [ rt ticks * turn-increment * 360 tilt-up ticks * turn-increment ] if flower-type = "Spiral" [ rt ticks * turn-increment * 360 tilt-up ticks * turn-increment * 360 ] if roll? [ roll-right ticks * turn-increment * 360 ] ] ask turtles [ fd step-size set size 0.6 * sqrt distancexyz 0 0 0 if distancexyz 0 0 0 > (max-pxcor - 0.5) [ die ] ] tick end ; Copyright 2003 Uri Wilensky. All rights reserved. ; The full copyright notice is in the Information tab.

There are 3 versions of this model.

## Attached files

File | Type | Description | Last updated | |
---|---|---|---|---|

Sunflower 3D.png | preview | Preview for 'Sunflower 3D' | about 11 years ago, by Uri Wilensky | Download |

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