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I'd like to make an LED blink with a varying frequency that depends on a voltage. I know about the 555's control pin, but I'd like the blinking to vary continuously, instead of switching between just two states.

The circuit will be used as an indicator to give the user a clue about how close to a target voltage he has adjusted a value. As a rough guideline, let's say "0Hz at 0V, 10Hz at 5V". The exact values are to be determined later, depending on the usefulness of this indicator.

I'm not very familiar with the 555, so I'm not quite sure where to start. I only ever built example circuits and changed part values to get the desired frequencies, but I guess so far I haven't learned enough about the chip to tackle this project.

I don't have to use a 555, however that's what I have at hand (and the problem smelled like 555). BUT please note that this has to be an analog (or discrete digital/74 logic) circuit. No microcontroller allowed. I already know how to solve this problem with a micro and I know that this is probably cheaper/easier/smaller with one, but I absolutely cannot have a software component for several reasons that are beside the point of this question.

So can someone please point me at an example circuit or give me some hints so I can learn what's needed to understand an build such an indicator feature?

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    \$\begingroup\$ A circuit which oscillates at a frequency that is dependent on a voltage is called a Voltage Controlled Oscillator or VCO. Use google to search for "VCO circuit" and press the images tab. Ignore the circuits with inductors as these are high-frequency VCOs, you want a circuit that uses resistor and capacitors for the timing. \$\endgroup\$
    – Bimpelrekkie
    Apr 15, 2021 at 14:32
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    \$\begingroup\$ Why do you think that the 555 control pin has just two states? It's an analog voltage. \$\endgroup\$
    – Dave Tweed
    Apr 15, 2021 at 14:35

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You can have a solid example circuit from here:

https://en.wikipedia.org/wiki/Voltage-controlled_oscillator

You basically want a voltage controlled oscillator. That means the frequency of operation depends on your reference voltage.

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Select a VCO (voltage-controlled oscillator) that has a sufficient dynamic range for your tuning requirement. (Note that using 0 Hz, as you mentioned, is effectively requiring infinite dynamic range. If you really need that mode, I suggest a bypass state in which you simply apply a static DC "on" or "off".) Since you're talking about relatively low frequencies (10 Hz max) you may need to follow your VCO with a frequency divider. Some VCO chips have these built in. Next, you may need to level-shift your VCO/divider output to the voltage level required to drive the enable pin of your LED driver.

There are also DCOs available (digitally-controlled oscillators), in case your control voltage happens to have a digital counterpart available somewhere in your system.

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