THE CHALLENGE (optimized for minimum size)

Author: Juhani Tapaninen @oh8mxl

System: C64 

Language used (name and possibly version): Basic V2

Length of source code: 93 bytes;   from separately written text file using ANSI encoding
(File size on disk: 1 block)

Length of executable file: 99 bytes;  command: PRINT 38911-(FRE(0)-65536*(FRE(0)<0)) 

Instructions on how to run the code:
- install vice c64sc
- attach disk image, drive #8: "oh8mxl_c64.d64"
- LOAD "OH8MXL",8,1
- RUN

Description of how the code works: 

The code for reference,

Packed: 
2 FORT=4TO17:S=INT(T/4):W=(T-S*4)*S+S-2ANDS<4:FORP=19-WTO21+W:PRINTTAB(P)"*";:NEXT:PRINT:NEXT

Unpacked:
2 FORT=4TO17:
S=INT(T/4):
W=(T-S*4)*S+S-2ANDS<4:
FORP=19-WTO21+W:
PRINTTAB(P)"*";:
NEXT:PRINT:NEXT

T loops the tree from top to bottom. The S equation gives the section number of the tree (1 to 4), W equation gives the half-width of tree (minus one) at current height. The P loop prints the stars centered to screen using efficient VDU command.

In more detail:

Variables:
T=Tree line number from top to bottom, 4 to 17
S=tree Section number 1 to 4 from top to bottom
W=half-Width of the tree at current line not including the trunk at the center of the tree -1
P=Position where to print the next star char

I started with 2 FOR loops, the first looping through 3 widening sections of the tree and second looping the four lines in each section, and adding the width of the stump separately. The width was calculated from the FOR variables. 

I was first working on BBC Micro Basic and after several iterations I noticed that the tree half-width not including trunk at highest 11 lines of the tree can be calculated in one FOR loop with equation
W=(T MOD 4)*(T DIV 4+1)+T DIV 4 (code has evolved since then, not usable anymore)

This equation was further reduced by using the tree section variable S and by changing the MOD and DIV commands to operands that the C64 Basic has.

Then, I noticed that I could add even the stump of the tree into the same width calculating equation with the "ANDS<4" logic operation part. For this to work I had to change the W variable not to be "tree half width w/o trunk" but "tree half width w/o trunk -1" since the logic operation returns 0 when we are at the stump.

Finally, tweaking the FOR loop to run from 4 to 17 instead of 0 to 13 took 2 bits away from the S equation, yay! (It had a "+1" part in it.)

It took many iterations during several evenings to reduce the code to current state. 

Please note that manually typing the code into C64 requires usage of a few shortcuts like ? for PRINT and fO for FOR and nE for NEXT not to exceed the 2 line limit on one BASIC command line.