Esaki effect implementation on simple oscillator circuit
IF the pinout is the same as the 


ONSemi P2N2222 data sheet here 


OR this 


TO18 cased @N2222A 


then you have the transistor C &amp; E reversed.   

That alone would completely prevent the circuit working as intended. 



Your photo is reasonably well taken (although you could have arranged it so that ALL connections were unambiguously visible) BUT it is very poorly presented.  

Just by cropping it to show only the relevant part you give people a much better idea of what you are doing.  Rotating it to be "square"  on is a bonus.
If you cannot do that look at fabulous free Irfanview - from here

Thusly:





Adding a few labels to show where eg power connects.
Showing where you THINK C &amp; E are, may help people see that they are not.





Finally [ :-) ], your enthusiasm in investigating such an unusual and interesting aspect of electronics is commendable, but your construction methods are unnecessarily untidy and it will take you LESS effort and give better results if you improve them. More could be said, but a few suggestions:


The transistor could have had all 3 leads plugged into the breadboard with the base not connected.  
Twisting the capacitor wires together is not advisable.  
Even if you do not cut the leads, bending resistor leads square so they sit flat and with an obvious orientation to where you are connecting you will be better able to see what you have done and to be sure it is what you intended.  
Connecting links for the power supply or battery to the horizontal "power rails" lets people see where power comes from ad allows you to know what is and connected to power and to disconnect and connect things easily and rapidly.




Note:

Circuit operation is somewhat component critical.
Note their comment: "If the resistor that charges the capacitor is too low in value (or if the power supply voltage is too high), the current through the transistor will not become low enough for the transistor to turn off. If the resistor that charges the capacitor is too high in value (or the power supply voltage is too low), the capacitor will not be able to charge to a high enough voltage to enable the transistor to turn on. This is because the transistor draws as small amount of current before switching on."