Recently, I'd been smitten by the thought of generating Flowers that don't fade & die away...those that i don't need to hurt and pluck too...!! (
As I admit, I'm a bit weird...esp. with flowers...& some people too...whom i treat/view like flowers...! :)
[Simply because they ARE so wonderful & precious fer Me..!]
Yes...I mean flowers generated with equations...! :)
Ever since I had seen things like the Cardioid in Engineering Mathematics, I'd been fascinated by them..but somehow, unfortunately, the fascination had got covered up in the sands of time...
But recently, i have been MAD.. .( as if I wasn't before..Ha ha ha !!)...!!
I did NOT realize JUSST How MAD i was, as i sat day & night...scribbling equations in Polar-co-ordinates & trying to vary different parameters & obtaining Different kinds of flowers, with different degrees of Symmetry, Numbers of petals, etc..!
And since a very Dear friend of mine loves ROSEs ( & oLL Flowers!)...well, I was hell-bent on somehow creating a mathematical PLOT that resembles a ROSE...but All my efforts went in vain...! :-/
There was a phase when I at-last gave-up...saying to my-self...that
"Everything in Nature can NOT be reduced to Mere Numbers & equations...!
We can NOT, & should NOT take away the Beauty of things by looking at them through the spectacles of Science...!"
But then, one day (or night..? I do not reckon the time..! )...
I came across this interview with my ever-effervescent friend Richard Feynman, where he spoke about His view of "The Beauty of a Flower" ...
He said --- Science (if done properly that is !! ), only serves to "ADD to" , and not "SUBTRACT frem" the Immense BEAUTY around us..! :)
Oh my ..!!
THAT was oLL i needed---some-One to boost my lonely morale...!! [
Now-a-nights (like Now-a-days--bear with my in-voluntary word-play..! ;)), it's usually ONLY Ghosts & my Nice friends frem the past, & my Dreams of the future..that listen to Me-moron...! Hmmm..! :)
I had earlier discovered an amazing equation to make a butter-fly (Can it ?? Can butter do..?! ;) )...but What i wanted was a ROSE...!! :-(
And late that night...as I sat varying parameters in an equation, I suddenly JUMPED out of my stupor..!
Because, I thought I saw something that resembled the complex, inward spiralling whorls of a ROSE flower..!! (Much like a Paper rolled into a cone...viewed from the top..!)
YES !! ---I shouted..!
My version of "Eureka!!" :) --also, I was on my bed in my pyjamas, rather than in a bath-tub in my birthday suit..hehehe..!! ;) Nevertheless, like Archimedes , I too was "Immersed"... in a kind of absent-minded thought...! :)
My equation-plot looked like a ROSE...!!!
And seeing it...I sat smiling, and... froze...!! :))
Ha ha ha !
Anyway, the equation & its details are as below... ( We can replace Sine by CoSine...no problemo...!)
And the ROSE ??
Well here she is...(in 2 colors...! :))
Also the Butterfly equation & the corresponding Butterfly are as below...!
As for the Rose...it was a pleasant surprise (as ALWAYS !!)...that I was NOT alone to have come to the island of this discovery...!!
That's an Amazing feeling...it's like discovering a lonely looking island...only to find some-one already there...HOW or WHY do different people grope & stumble upon the same Beautiful (or otherwise) islands, Truths, ideas, concepts, etc..!?!? :)
Whatever it is...me SO glad that I am NOT addicted to Google-ing immediately...ELSE...I would not have experienced what Feynman called..."The Pleasure of Finding Things Out" ..!! :)
I learnt that an Italian mathematician, Guido Grandi had studied the curves he had lovingly named "rhodonea"..!
THANK you SO MUCH for Listening to Me-MORON & my narration of what is surely the makings of a StubBORN (he)ART. . .& its Un-FaDing MAdness...!! :)
Take Care then...!
And Keep Smiling...with your Loved & Loving ones...!
Lots o Loooove & Best Wishes,
mor(e)on "rags". . . :)
Planet (H)eart(h) #####################
And NOW, for a Hilarious ( & True..?! ;) ) explanation of another question..!
Question ? "WHY do MEN Like Expensive things..?"
Answer ? "Because WOMEN Do." ;-)
Enjoy the below cartoon, courtesy Hart