Spiral Art

The basic idea behind a spiral is to parametrize like this.......

x=rcosθy=rsinθx = r \cos \theta \\ y = r \sin \theta

....and then gradually decrease the radius as the angle increases. To make things more interesting, you can put sinusoidal variation in the radius too, with different harmonics thrown in to create different effects. The harmonics are added so that their magnitudes are inversely proportional to their frequency, relative to the base frequency. For example, a sinusoidal term with a frequency three times that of the base term has a magnitude one third that of the base term.

I have posted two spirals: one with even harmonics and one with odd harmonics. The code to generate these is also attached. Click the images to enlarge them.

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import math

r = 20.0
theta = 0.0

dr = 0.005
dtheta = 2.0*math.pi/400.0

choose = 0

while theta <= 20.0*math.pi:

    if choose == 0:

        # Even harmonic spiral 
        x = r*(1.0 + 0.2*math.sin(20.0*theta) + 0.1*math.sin(40.0*theta) + 0.05*math.sin(80.0*theta))*math.cos(theta)
        y = r*(1.0 + 0.2*math.sin(20.0*theta) + 0.1*math.sin(40.0*theta) + 0.05*math.sin(80.0*theta))*math.sin(theta)

    if choose == 1:

        # Odd harmonic spiral
        x = r*(1.0 + 0.2*math.sin(20.0*theta) + 0.0667*math.sin(60.0*theta) + 0.04*math.sin(100.0*theta))*math.cos(theta)
        y = r*(1.0 + 0.2*math.sin(20.0*theta) + 0.0667*math.sin(60.0*theta) + 0.04*math.sin(100.0*theta))*math.sin(theta)

    print x,y

    r = r - dr
    theta = theta + dtheta

Note by Steven Chase
1 month ago

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Comments

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Top Newest

@Neeraj Anand Badgujar Per your request

@Karan Chatrath In case you are interested

Steven Chase - 1 month ago

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@Steven Chase Sir .Thanks Yeah it's also awesome. But I like your profile images more than this. They were more crazy according to my opinion.

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Creating the profile pic must have been much harder, due to the wireframe and the 3d aspect of it, that too on python.

Krishna Karthik - 1 month ago

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@Krishna Karthik Yeah, the helix was a much bigger undertaking

Steven Chase - 1 month ago

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Yeah and the rendering time without GPU wow...

Krishna Karthik - 1 month ago

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Ha that's really cool! I really like python. Try to paint a Mandelbrot Set!

Krishna Karthik - 1 month ago

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Here you go

https://brilliant.org/discussions/thread/plotting-the-mandelbrot-set-roughly/

Steven Chase - 1 month ago

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I think the second spiral looks the best. I really love how it spirals inward.

Krishna Karthik - 1 month ago

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