I plan to make a 6x6 white LED (3v, 20mA) matrix. All of them will be controlled at the same condition.
I would be grateful if you could give me some advice.
So you will have 36 white LEDs all the same intensity at the same time ?
What voltage do you have available to power these again ?
I want to use 12v adapter for power supply.
My plan is each series will have 3 LEDs and I will have 12 series in parallel.
R1 C1 will have to be picked, probably by experimentation.
A resistor across C1 may be needed to discharge C1 for the response you need.
Suggest you use 24VDC.
Placing LEDs in parallel will not give repeatable currents in each string.
In post #23 you would need 6 transistor circuits.
So that poor little 0.5W resistor is going to dissipate more than 1W?
@LarryD hi Larry; yes that was my first thought.
the transistors would need to have very high gain though, so I'd consider a pnp emitter follower to buffer the 1k/C1 filter.
Also for sure I'd go for a 24V / 6 series LEDs as easier and simpler , and justa 240 ohm fixed R (replacing r2+r3).
According to my measurements, the voltage is 4v. I estimate the power is less than 0.1W.
If there are mistakes, please let me know.
Thank you.
I don't like using a single resistor for parallel LEDs but...
If it has 20mA per row, and 12 rows, so 240mA current through the resistor.
If resistor measuring 4V, consumes the resistor's power is about 1W. 
As @LarryD says, one row requires one current limiting.
Thank you. I got it.
This is just a test circuit, I want to see if I can achieve the expected light intensity. The LEDs are not running at full capacity, the amperage is only about 2mA.
I understand this is a bad design, I will fix it.
Things don't add up. If this is a test to see if you can get the desired intensity, then why run the LEDs at a fraction of the power? Is that 2mA per string, or for all strings combined?
Anyway, I stand by my earlier suggestion of using a dimmable led driver; it's the most straightforward approach. The datasheet of the selected part always has a formula for calculating the inductor needed for a particular use case.
It is 2mA per string. I am trying to culture bacteria and test their growth under different conditions. The test circuit is used to generate optimal light intensity to test if bacteria can grow under this type of LED light, that why just a fraction of the power was used.
I'm also searching on dimmable led drivers. But since I don't have much knowledge about electronics, it takes some time. Thank you for the suggestion.
Okay, yeah, I understand the experiment. We had a little miscommunication; I thought you meant that you were trying to find the maximum light output you could get from this led setup, but you were stating the purpose of the bacteria experiment.
I also understand that the electronics stuff is basically just a side-show for you; it's likely not your core business/competence. Nothing wrong with that. Would it be permissible and possible in your situation to team up with someone who could handle the electronics part for you? It would save you a lot of time and for someone with some experience with electronics, it would probably be something like a 1-day job to make an experimental setup for you.
I'm in the early stages of the experiment. If it succeeds, I may be able to get someone with expertise to optimize my circuits. 
And not only this project, I have an interest in electronic circuits (although that is not my major), I want to know more about it. btw, one of my hobbies is mechanical keyboard, I hope one day I can make one by myself.
From the study you linked it seems the pulsed light has quite minor effect on the growth of the flowers. You are still worried about this effect. Did you consider the light intensity from LEDs does not change linearly with current? To get precise light intensity you need some feedback. And LED light is not homogenous in all directions - maybe you should measure intensity in more than one point. And each LED has slightly different characteristics.
Maybe it is no problem but I think it may be easier and more reproducible to use high frequency PWM and change the duty instead of trying to change the light output by controlling current.
I wonder if that marginal non-linearity is problematic, though. See e.g. Lumileds datasheet for LUXEON 2835 product family (a fairly randomly chosen white power LED), page 13: quite linear relationship between current and light output, which only loses tracking somewhat at low levels. Again, I doubt it would be a problem for this experiment.
PWM is indeed straightforward, but does not solve your relevant remarks on effective illumination of a sample which also depends on e.g. angle of incidence and the radiance pattern of the emitter. However...we can tell from the perfboard prototype that apparently the use of a fairly diffuse light source is considered, and that would deal with this particular concern fairly well.
The main issues remains: can it be expected that the bio-sample responds differently to pulsed light vs. continuous light? Fact of the matter is: we don't know. I've seen people in this thread taking a stab at it, but I find that kind of conjecture very doubtful. On the one hand, we know of several processes that seem to "don't care" about pulsed vs. continuous. On the other hand, I certainly know of chemical processes where there IS a difference (see e.g. reciprocity failure in photography). Where the photo-sensitive processes inside bacteria fit here, we just don't know. For a research setting, I think it would be very risky from a methodological viewpoint to just assume it doesn't matter.
This is exactly my problem. Some people have proven it has significant effects, so I cannot simply ignore it. Maybe when we use very high frequency (eg 1MHz) the effect of PWM is negligible compared to continuous light. But if I want to accept it, I have to prove it. That is another story.
About MP24894, can you give me some similar products? Just in case I can't buy it. Thank you.
It is just needed to consider what is worse.
With PWM the result of the study will be "Growth speed vs. PWM duty"; with current control it will be "Growth speed vs. LED current" or worse - "Growth speed vs. Arduino PWM duty": with simple circuit you don't know how closely current matches Arduino PWM duty and light output matches current. I assume light output will follow the Arduino PWM duty "roughly linearly" while growth speed will also follow light output "roughly linearly". It will be VERY difficult to determine if the observed difference is due to electronic or biologic non-linearity.
With PWM it is simpler - you can simply verify the duty by a scope (or at least a DMM) and any observed variability is due to the bacteria. Of course it needs to be determined if it is caused by the average light output or the duty itself has some consequences.
EDIT: Tip for your next study 
With average light output fixed what happens when you change the PWM duty?