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spiral curve frequency control in Houdini

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Hello, I am trying to create a spiral curve with frequency control. 

I have used Sin for x-axis and Cos for y-axis to create a spiral. 

when I tried to multiply the frequency with a 0-1 ramp, the result was far from what I have expected. (shown in my screenshot) 

I am trying to make the frequency high at the both ends and low in the middle. 

Can someone tell me what I am doing wrong and how I can fix it to work properly? 


Thank you. 

spiral frequency.PNG

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