## New Sunflower Applet: Fibonacci and the Golden Angle

Here’s a new applet I created (simply because I haven’t made one in a while and thought it’d be fun). Look at how different angles result in different sunflower configurations by clicking the picture below.

Why is the golden angle 137.5 degrees? If you’re struggling to figure it out based on the standard derivation of the golden ratio then there’s a few videos on youtube that’ll help.

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### 3 Responses to New Sunflower Applet: Fibonacci and the Golden Angle

1. Nice graphic – could you explain how the pattern is being generated? r = radius, but then how do the alpha and angle values generate the circles?

2. Hey,

The angle which the point is being rotated through is of course not alpha (the slider). When you put the input angle into the box (called that ang in the applet), the angle that the point is being rotated around by is theta = ang*alpha. Hence if ang=137.5 then the first rotation will of course be theta=137.5*1 degree, the second will be theta=137.5*2 degrees, so the rotation angle is always a multiple of the input angle.

The points appear due to the sequence function – it basically fixes the point every time it is rotated. If you download the applet then you’ll see the Sequence function is simply the original point with the sequence variable (usually use i for this) ‘artificially’ added in.

Hope that helps.

3. thanks – that make sense 🙂