Spiral Art

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

$x = r \cos \theta \\ y = r \sin \theta$

....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.

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

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Easy Math Editor

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`italics` or `_italics_`	italics
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Note: you must add a full line of space before and after lists for them to show up correctly
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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

@Neeraj Anand Badgujar Per your request

@Karan Chatrath In case you are interested

Steven Chase - 1 year, 1 month ago

@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.

A Former Brilliant Member - 1 year, 1 month ago

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 year, 1 month ago

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

Yeah and the rendering time without GPU wow...

@Steven Chase when I copied this code and run in my computer and plotted in excel I get this image

A Former Brilliant Member - 11 months, 3 weeks ago

Hmmm... that's interesting... what do you think the error might be?

Krishna Karthik - 11 months, 3 weeks ago

@Krishna Karthik Bro I don't know, can you run in your computer and reply me what you are getting. Thanks in advance

@A Former Brilliant Member – Of course! cheers.

@Krishna Karthik – @Krishna Karthik bro i am waiting for your comment .what are you getting while running the above code ??
thanks in advance.

@A Former Brilliant Member – I get the same thing as Steven did. I think you have copied the code wrong.

@Krishna Karthik – @Krishna Karthik ok bro let me try again. thanks

btw if you don't mind ,please call him as Steven sir .they are older than us.

@A Former Brilliant Member – Bro, this is the internet. People are called informally on the internet. Unless they specifically say against that, I am going to just call them by first name.

I think it's some sort of an Indian custom to suffix with sir for someone older. Maybe I'll refer to him as sir if I directly address them.

@Krishna Karthik – @Krishna Karthik as you wish bro.it is your choice .

He has helped me so much in physics and maths ,so its my respect for him

@A Former Brilliant Member – Very true. He has pointed me to so many resources, really great person. He helped me with classical mechanics and inspired me to learn numerical technique. I do respect him a lot. I will address him as sir when I speak to him. Thanks bro, cheers! :)

@A Former Brilliant Member – Oh, I think I noticed the error and why the graph is not showing the correct thing. Have you perhaps only chosen one of the columns? Make sure you select both and look at the line, not the line with dots (as it will clutter).

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

Here you go

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

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

@Steven Chase sir the code which you have provided above.
i run this code and when plotted in excel and was not giving the figure which is above .
as obvious Thanks in advance

Highlight both columns and then plot as a scatter with smooth lines

Steven Chase - 11 months, 3 weeks ago

precicely, sir. That's what I think the error is too. Scattering with dots will create clutter too.

Yup, buddy, I think you haven't underlined both columns. Plot with smooth lines too.

@Steven Chase sir i have highlighted both columns many times
I am getting this only

Nope, it still only shows one column.

put a variable (x) on the x column, $y$ on the $y$ column ABOVE the columns; click on $x$ , hold, and drag it all the way down to the end and click on the smooth line chart.

You should have names above each column. The column on the left will automatically be identified as the independent variable, and the right the dependent.

Click on the left column's name and drag it down, highlighting both columns.

@Krishna Karthik thanks sir but why image above is more clear than my pC image

@A Former Brilliant Member – You can re-size the plot and make the lines thinner

@Steven Chase – Ah, I was having the same problem too with thick lines. Thanks sir!

@Steven Chase – @Steven Chase sir which option should i choose to make it thin

Hey, do you use Windows 7 or 10?

@Krishna Karthik 7

@A Former Brilliant Member – Yeah, I thought so. Is that a Dell laptop?

@A Former Brilliant Member – You should upgrade it. I kinda miss Windows 7 though lol now that I upgraded my PC... =..(

@Krishna Karthik – @Krishna Karthik windows 10 have more features than 7?
if yes how can i upgrade

@A Former Brilliant Member – Windows 7 is really outdated now; but Windows 10 is expensive. It's not extremely worth it or anything, but next time you get a PC you will automatically have Windows 10 with it =)

@Steven Chase yeah now it is coming

Perfect! Good stuff mate.

Yeah, the reason we are seeing the visible damping in x and y is because of the spiral.

@Steven Chase sir how do you export that image ???

Hit the print screen button and then paste it into MS Paint. Then you can crop out the stuff you don't want

Ah, that is much better than taking a cropped screenshot. It gets so low res for me when I take a cropped screenshot. Thanks for suggesting me the better alternative. Will use MS paint.

Yeah, that's what I was wondering as well. I just take screenshots.

@Krishna Karthik taking screenshot loses the quality if image

You can put it onto MS Paint and crop out the rubbish. That's a better way. No losing of res.

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$